CN103023703B - Network timely reliability accelerated test method based on M/M/s queuing model - Google Patents

Abstract

The invention discloses a network timely reliability acceleration test method based on the M/M/s queuing model, which comprises the following steps: Step 1: According to the delay failure mechanism of the communication network queuing model, the composition of the queuing model is obtained, and the service intensity requirement is determined ; Step 2: obtain the network timely reliability model; Step 3: obtain the reliability acceleration model based on similarity theory; Step 4: carry out the network timely reliability acceleration test; The reliability acceleration test method can effectively solve the problems of the current network reliability test, such as too long time and high cost, or insufficient sample size and low confidence in short-term tests, thereby improving test efficiency.

Description

Accelerated Test Method of Network Timely Reliability Based on M/M/s Queuing Model

technical field

The invention belongs to the technical field of network communication and reliability, and in particular relates to a network timely reliability acceleration test method based on an M/M/s queuing model.

Background technique

With the continuous development and application of network technology, the scientific understanding of the quantitative and qualitative characteristics of the network has become an extremely important challenging topic, even called "the new science of the network". With the popularization of network usage and the increase of network load, the timely reliability caused by congestion has become an important issue in the understanding of network quantitative characteristics.

Before a new network is built and a new service is put into use, testing is an important way to assess network reliability. However, the network task period is generally long. In order to effectively expose faults, the network reliability test time is often several times the task period (Reference [1]: Zhang Jiantao, Zhang Jian. Comprehensive reliability test and inspection of military communication network [J ]. Electronic Product Reliability and Environmental Testing, 25(2), 2007: 19-22), which directly leads to a long development cycle. In order to quickly expose design flaws in reliability tests and determine the reliability level of the network, it is necessary to adopt accelerated tests to increase the number of cycles per unit time and accelerate the emergence of failure modes. Acceleration model is the premise of designing acceleration test. For the timely reliability of the network, the failure mode is too long delay, and the queuing mechanism of the network provides support for exploring the delay failure mechanism and determining the acceleration model. Similarity theory is a theory for studying the similarity principles of various physical processes in nature and engineering, and is the theoretical basis for determining the acceleration model.

Most of the existing acceleration tests and acceleration models are in the field of hardware, and there is no exploration of reliability acceleration models and test methods for communication networks. It is still unable to solve the problems of too long time and high cost of network reliability test, or insufficient sample size and low confidence of short-term test.

Contents of the invention

The purpose of the present invention is to solve the problem that the reliability test time is too long or the confidence level of the short-term test evaluation is low, and proposes a network timely reliability acceleration test method based on the M/M/s queuing model. The derivation and verification of the model, and the formulation of the accelerated test plan for the timely reliability of the network.

A network timely reliability acceleration test method based on M/M/s queuing model, comprising the steps:

Step 1: Obtain the composition of the queuing model and determine the service intensity requirements according to the delay fault mechanism of the queuing model of the communication network;

Step 2: Obtain the timely reliability model of the network;

Step 3: Obtain the reliability acceleration model based on the similarity theory;

Step 4: Carry out network timely reliability acceleration test;

Advantage and positive effect of the present invention are:

(1) The method of the present invention proposes a network reliability acceleration model based on queuing theory in time, and deduces and verifies the network reliability acceleration model of the M/M/s queuing system under the guidance of the similarity theory, which is the similarity theory in the acceleration test Another application of , and also another application of network flow, is the core of the accelerated test and the model basis for planning the accelerated test.

(2) The method of the present invention establishes a theoretical basis for the accelerated test method of network reliability: according to the deduced accelerated model, the test method of the communication network can be further determined. This is the promotion of the product accelerated life test on the network object, which can effectively solve the current The network reliability test time is too long, the cost is too high, or the sample size of the short-term test is insufficient, and the confidence level is low, so as to improve the test efficiency.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is that OPNET among the present invention sets up M/M/s queuing model example figure;

Fig. 3 is an exemplary diagram of a communication network topology in an embodiment of the present invention.

Detailed ways

The present invention will be further described in detail with reference to the accompanying drawings and embodiments.

The present invention proposes a network timely reliability acceleration test method based on the M/M/s queuing model, comprising the following steps:

Step 1: According to the delay fault mechanism of the queuing model of the communication network, the composition of the queuing model is obtained, and the service intensity requirement is determined.

Specifically include the following steps:

Step 1.1, obtaining the composition of the queuing model: the composition of the queuing model consists of input process, arrival rules, queuing rules, service organization structure, service time, and service rules.

The M/M/s queuing model means that the input process is a negative exponential distribution with a data arrival time interval of λ, the arrival rule is a single arrival of data, the total data source is an infinite source population, the queuing rule is first-come-first-served, and the service organization structure is s service desks are connected in parallel, the capacity is infinite, the service time obeys the negative exponential distribution with the average service time μ, and the service rule is a queuing model of serving a single data at a time. (Reference [2] Tang Yinghui, Tang Xiaowo. Queuing Theory-Basic and Analysis Technology [M]. Beijing: Science Press, 2006:33) When the network data packet arrives, if there is an idle service desk in the switch, it will start to provide Data exchange service, otherwise wait in queue until all previous data packets complete data exchange. If the stay time is too long and the fault criterion is reached, a delayed fault occurs.

Step 1.2, determine the service intensity requirement of queuing model: when ρ _s =λ/sμ<1, ρ _s represents queuing model service intensity, and queuing model can reach statistical balance, and stay time constitutes probability distribution, is the precondition of the inventive method ; Otherwise, more and more data will arrive and accumulate, the queuing model will not be able to reach a steady state, and the queuing delay will increase with time. In this case, it is meaningless to discuss delay faults.

Step 2: Obtain the timely reliability model of the network;

Specifically include the following steps:

Step 2.1, determine the expression of network timely reliability. Reliability is a measure of reliability in probability. The expression of timely reliability in the network is:

R=P{D≤D _max } (1)

In the formula, D represents the network data transmission delay, D _max represents the maximum delay allowed by the user, that is, the failure criterion, R represents the reliability of the network in time, and P represents the probability that the actual network delay does not exceed the maximum delay allowed by the user .

Step 2.2, determine the residence time distribution function, the residence time distribution function of the queuing model of M/M/s is:

The residence time distribution function of the M/M/s queuing system can be obtained according to the reference [2] Tang Yinghui, Tang Xiaowo. Queuing Theory-Basic and Analysis Technology [M]. Beijing: Science Press, 2006:33.

$\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}\begin{array}{}\end{array}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;t</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\mathrm{<span\; class="notranslate">\; \&mu;t</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;t</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;t</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In the formula: W is the residence time of the data packet in the model, which is the sum of the waiting time and the service time. t is the time independent variable. W(t) represents the probability that the data packet stays in the model W for no more than t. When the queuing model is determined, the number of service desks is s, s is a constant, p _s is the probability that the number of customers in the model is s, and the expression can be recorded as p _s =f(ρ).

In fact, Equation (2) is an expression of the timely reliability of the communication network. In formula (2), t is a given delay threshold D _max . Combining formula (1) and formula (2), the network timely reliability model can be expressed as:

$\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}\begin{array}{}\end{array}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; \&mu;D</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;D</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;D</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula: R is the real-time reliability of the network.

Step 3: Obtain the reliability acceleration model based on the similarity theory;

Specifically include the following steps:

Let equation (3) be the reliability model of the original network, then the reliability model of the similar network is:

${\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>\frac{{{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; .</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula: R' is the real-time reliability of the similar network, D' _max represents the maximum delay allowed by the user, λ' is the arrival time interval of similar network data, μ' is the average service time of similar network, and the number of service stations is s.

Let the number s of servers in the similar network not change, considering p _s = f(ρ), there are actually 4 physical quantities in formula (3), namely R, λ, μ and D, let the similarity constants be c _R , c _λ , c _μ and c _D respectively, which represent the parameters in the similar network The change factor from the corresponding parameter in the original system, namely:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; R</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; R</span>}\\ {\mathrm{<span\; class="notranslate">\; \&mu;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}\\ {\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; ma</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

For the sake of simplicity, it is required that the reliability R' in the similar network remains unchanged from the reliability R in the original network, that is: c _R = 1; and the similarity constant between the average data arrival interval time and the average service time is equal, that is, c _μ ＝c _λ ; according to the first theorem of similarity, and the simultaneous equations (3), (4) and (5), it can be obtained: c _μ ·c _D ＝1

Thus, three similar criteria of the M/M/s queuing model are obtained, which are reliability acceleration models:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

As the intensity of network data arrival increases, the number of data packets arriving within the same time period increases, and the amount of reliability information increases. In order to meet the data volume requirements required for reliability test censoring (reference [3] GB5080.5-85. Verification test plan for the success rate of equipment reliability test [S]. The Ministry of Electronics Industry and the Ministry of Aerospace Industry of the People's Republic of China. 1985:5-9), after the arrival strength of network data increases by c _λ times, the test duration can be reduced by c _λ times, and the data volume of the two tests remains unchanged. That is, the relationship between the test duration and the network data arrival intensity is:

c _λ =t/t′ (7)

In the formula: t is the duration of the original network test, and t′ is the duration of the similar network test.

Step 4: Apply the OPNET simulation platform to verify the reliability acceleration model;

Specifically include the following steps:

Step 4.1, establish M/M/s queuing model with OPNET;

Step 4.2, design the reliability model of the original network based on the M/M/s queuing model, select λ, μ and D, and the test duration t, and perform OPNET simulation;

Step 4.3, design the reliability model of the similar network based on the M/M/s queuing model, select the corresponding similarity coefficients c _λ , c _μ and c D of λ, μ and _D according to formula (6), and determine the reliability model of the similar network Parameters, as well as the test duration t', satisfy t'=t/c _λ , and carry out OPNET simulation;

Step 4.4, calculate the timely reliability of the original network and the similar network, and compare them. In the simulation, the statistical method of network real-time reliability is:

R=N _n /N _t (8)

In the formula, N _t represents the total number of data packets transmitted by the network, and N _n represents the number of data packets whose network transmission delay does not exceed the maximum delay D _max allowed by the user, that is, the number of timely transmitted data packets.

The reliability is calculated at the time t corresponding to the original network and the similar network, and the mean square error is calculated. If the reliability mean square error of the original network and the similar network are all within the acceptable range in the simulation of multiple failure criteria and stress increase multiples, then the accelerated model is considered correct and reasonable.

Step 5: Carry out network timely reliability acceleration test;

Specifically include the following steps:

Step 5.1, determine the number of network data collection, assume that the network model is M/M/s queuing model, delay faults obey the binomial distribution, value inspection upper limit R, discrimination ratio D, producer risk α and consumer risk β. Then, the amount of time delay information required to collect data packets at least in the reliability identification test can be checked.

In step 5.2, the acceleration test parameters are obtained. If the original network task profile parameters and delay thresholds are λ, μ and D _max , the test duration is t. Select the similarity coefficients c _λ , c _μ and c _D corresponding to λ, μ and D _max according to formula (6), and then λ', μ' and D' _max can be obtained. According to the accelerated test parameters, a reliability accelerated test with a duration of t'=t/C _λ is carried out to obtain the timely reliability of the accelerated network. This value can be considered to be the same as the timely reliability of the original network, that is, the timely reliability of the original network can be obtained.

Example:

The simulation part in the embodiment of the present invention takes the OPNET queuing model shown in Figure 2 as an example, and specifically sets forth the simulation verification of the acceleration model in the method of the present invention, and the test part takes the actual communication network shown in Figure 3 as an example, and sets forth concrete and reliable Accelerated testing program.

There are three nodes in Figure 2, which are the data sender (src), the queuing mechanism (queue) and the data receiver (sink). The data packet arrival interval and the distribution of data packet length can be set at the sending end, and the queuing rules and service time distribution can be set at the queuing mechanism.

The network timely reliability acceleration test method based on the M/M/s queuing model of the present invention, the steps are as shown in Figure 1, wherein steps 1, 2, and 3 are the same as in the specific implementation mode, and will not be repeated here, steps 4 and 5 The specific method is as follows:

Step 4: Apply the OPNET simulation platform to verify the reliability acceleration model, the specific method is:

Step 4.1, use OPNET to establish the M/M/s queuing model, as shown in Figure 2: Here, the data arrival interval and data packet length distribution at the src data sending end select exponential negative exponential distribution, and the processing model of the queue queuing mechanism selects acb_fifo_ms.

Step 4.2, design the reliability model of the original network based on the M/M/s queuing model, select certain λ, μ, t and D, and conduct OPNET simulation: In this verification case, the network service rate is 9,600bit/s, The data arrival intensity follows a negative exponential distribution with an average value of 2.67packet/s, the data packet size obeys a negative exponential distribution with an average value of 9,000 bits, and the number of service stations is 5, that is, ρ _s =0.5. Assuming that the network delay fault obeys the binomial distribution, take the upper limit of inspection R=0.999, the discrimination ratio D=1.50, and the risk α of the producer and the risk β of the user are 10%. Then, in the reliability identification test, at least 32922 data packets need to be collected The delay information of , so at least 3.425 hours of simulation is required to arrive at this number of packets. Applying OPNET simulation for 4 hours, a total of 35789 data packets were collected.

Step 4.3, design the reliability model of a similar network based on the M/M/s queuing model, select c _λ , c _μ , c _t and c _D according to the rules of formula (6), and determine the reliability model parameters of the similar network and the test duration t', carry out OPNET simulation: take c _μ =c _λ =4, C _D =c _t =0.25, t'=1 hour, the state at t ₀ is the same. In this way, the network service rate is 19200bit/s, the average data arrival time interval obeys the negative exponential distribution with the mean value of 5.34packet/s, and the data packet size obeys the negative exponential distribution with the mean value of 9000bit. According to the accelerated model, a total of 36,000 data packets were collected after 1 hour of simulation.

Step 4.4, calculate the timely reliability of the original network and the similar network, and compare them. In the simulation, the statistical method of network real-time reliability is:

R=N _n /N _t (8)

In the formula, N _t represents the total number of data packets transmitted by the network, and N _n represents the number of data packets whose network transmission delay does not exceed the maximum delay D _max allowed by the user, that is, the number of timely transmitted data packets.

In the original network and the similar network at intervals of 8 minutes and 2 minutes respectively, calculate the point estimation value of the end-to-end timely reliability of the network according to formula (8), and calculate the original network and the similar network under different delay failure criteria The mean square error of in-time reliability is shown in Table 1. In this embodiment, when the original network delay threshold varies from 2 to 5 s, the mean square error is less than 0.02, indicating that the method has strong applicability under different values of the delay failure criterion. As the delay threshold increases, its mean square error becomes smaller and smaller, and the similarity in reliability between the original network and the similar network is higher. Table 1 also discusses the absolute errors of the timely reliability of the two networks, both of which are less than 3×10 ^-3 , and the stricter the delay fault threshold, that is, the smaller the absolute error for the network with higher calculated reliability, the Accelerated models are more accurate.

Table 1 The influence of fault criteria on the acceleration model

Table 2 further discusses the mean square error of the reliability of the original network and the similar network under different stress multipliers. Here, when the stress multiplier changes from 2 to 12 times, the mean square error and absolute error of the two networks in time reliability do not change much. This shows that the multiplier of network stress does not affect the similarity in reliability between the original network and the similar network.

Table 2 Effect of stress increase multiple on acceleration model

In the above analysis, since there are only about 1200 data in each Δt time period (Δt=8min in the original network, Δt=2min in the similar network), there is still a certain error in the timely reliability of the two networks, and the absolute error is in Around 10 ^-4 . If the amount of data per unit time is increased, the error will be greatly reduced. Table 3 shows the impact of the number of service desks on similar networks. It can be seen that the change of the number of service desks does not affect the applicability of the method.

Table 3 The influence of the number of service desks on the acceleration model

Step 5: Carry out network timely reliability acceleration test, corresponding to the theoretical model in Figure 2, the test part takes the actual communication network shown in Figure 3 as an example, and elaborates the specific reliability acceleration test plan:

The communication network in Figure 3 consists of two end systems and a switch. The end system can be a system with specific functions, such as the AFDX avionics system, or it can be an ordinary notebook in the local area network. Here, the end system mainly sends and receives data, and the data flow sent by end system A is finally received by end system B through the switch.

Step 5.1, determine the quantity of network data collection, assuming that the time delay of data packets passing through the switch is M/M/s queuing model, and the delay fault obeys the binomial distribution. According to the requirements of the user, if the inspection upper limit R=0.999, the identification ratio D=1.50, the risk α of the producer and the risk β of the user are 10%. Then, through relevant standards (reference [3] GB5080.5-85. Verification test plan for equipment reliability test success rate [S]. Ministry of Electronics Industry and Ministry of Aerospace Industry of the People's Republic of China. 1985:5-9) can check In the reliability identification test, it is required to collect at least the number of delay information of data packets, which is 32922 data packets here.

Step 5.2, obtain the acceleration test parameters, if the original network task profile parameters and the delay threshold are λ=1packet/s, μ=2packet/s and D _max= 50ms, and the test duration is t=9.145h or more, at least 32922 can be collected data pack. Select the similarity coefficients c _λ , c _μ and c _D corresponding to λ, μ and D _max according to formula (6), and then λ', μ' and D' _max can be obtained. For example, c _μ =c _λ =4, c _D =0.25, D _{max =} 12.5ms. Carry out a reliability acceleration test with a duration of t'=t/c _λ =9.145/4=2.23h according to the acceleration test parameters, measure the time delay of each data packet passing through the switch through hardware tools or software, and you can get the specified not less than Latency data for 32922 packets. Using these obtained delay data, combined with formula (8), the timely reliability R of the accelerated network can be calculated. Assuming it is 0.99, this reliability value can be considered to be the same as that of the original network, that is, the original network’s The in-time reliability is 0.99.

Claims (1)

1., based on the timely reliability accelerated test method of network of M/M/s queuing model, comprise the steps:

Step one: according to the delay fault mechanism of communication network queuing model, obtains the composition of queuing model, determines service intensity requirement;

Specifically comprise the steps:

Step 1.1, obtains the composition of queuing model: the composition of queuing model is made up of input process, arrival rule, queue discipline, service organization's structure, service time, service regulation;

M/M/s queuing model, represent that input process is the quantum condition entropy that data are spaced apart λ the time of advent, arriving rule is the single arrival of data, data source is totally that infinite source is overall, queue discipline is First Come First Served, and service organization's structure is s information desk parallel service, and capacity is infinite, service time is obedience average service time is the quantum condition entropy of μ, and service regulation is the queuing model of once serving individual data; After network packet arrives, as switch presence service platform is idle, then starts to provide data exchange service, otherwise wait in line, until packets all above completes exchanges data; If residence time is long, when reaching failure criterion, then there is delay fault;

Step 1.2, determines that the service intensity of queuing model meets ρ _srepresent queuing model service intensity;

Step 2: obtain the timely reliability model of network;

Specifically comprise the steps:

Step 2.1, determines the timely reliability expression of network, and reliability expression is in time in a network:

R＝P{D≤D _max} (1)

In formula, D represents network data transmission time delay, D _maxrepresent the maximum delay that user allows, namely failure criterion, R represents the timely reliability of network, and P represents that the actual time delay of network is no more than the probability of the maximum delay that user allows;

Step 2.2, determines sojourn time distribution function, and the sojourn time distribution function of the queuing model of M/M/s is:

$W\left(t\right)=P(W\&le;t)=\left\{\begin{array}{c}1-e^{-\mathrm{\&mu;t}}[1+\frac{p_s}{1-{\mathrm{\&rho;}}_s}\mathrm{\&mu;t}],\mathrm{\&rho;}=s-1,\\ 1-e^{-\mathrm{\&mu;t}}-\frac{p_s}{(s-\mathrm{\&rho;}-1)(1-{\mathrm{\&rho;}}_s)}[e^{-\mathrm{\&mu;t}}-e^{-\mathrm{\&mu;}(s-\mathrm{\&rho;})t}],\mathrm{\&rho;}\&NotEqual;s-1.\end{array}\right.---\left(2\right)$

In formula: W is the residence time of packet in model, for the stand-by period and service time sum; T is time independent variable; W (t) represents that the residence time W of packet in model is no more than the probability of t; when queuing model is determined, service number of units is s, s is constant, p _sfor Number of Customers in model is the probability of s, expression formula can be designated as p _s=f (ρ);

In fact, formula (2) is exactly the expression formula of the timely reliability of communication network; In formula (2), t is exactly given delay threshold D _max; Convolution (1) and formula (2), the timely reliability model of network can be expressed as:

$R=P(D\&le;D_{\max })=\left\{\begin{array}{c}1-e^{-{\mathrm{\&mu;D}}_{\max }}[1+\frac{p_s}{1-{\mathrm{\&rho;}}_s}{\mathrm{\&mu;D}}_{\max }],\mathrm{\&rho;}=s-1,\\ 1-e^{-{\mathrm{\&mu;D}}_{\max }}-\frac{p_s}{(s-\mathrm{\&rho;}-1)(1-{\mathrm{\&rho;}}_s)}[e^{-{\mathrm{\&mu;D}}_{\max }}-e^{-\mathrm{\&mu;}(s-\mathrm{\&rho;})D_{\max }}],\mathrm{\&rho;}\&NotEqual;s-1.\end{array}\right.---\left(3\right)$

In formula: R is the timely reliability of network;

Step 3: obtain reliability acceleration model based on similarity theory;

Specifically comprise the steps:

If the reliability model that formula (3) is primitive network, then the reliability model of similar network is:

$R^{\&prime;}=\left\{\begin{array}{c}1-e^{-{\mathrm{\&mu;}}^{\&prime;}{D^{\&prime;}}_{\max }}[1+\frac{{p^{\&prime;}}_s}{1-{{\mathrm{\&rho;}}^{\&prime;}}_s}{\mathrm{\&mu;}}^{\&prime;}{D^{\&prime;}}_{\max }],{\mathrm{\&rho;}}^{\&prime;}=s-1,\\ 1-e^{-{\mathrm{\&mu;}}^{\&prime;}{D^{\&prime;}}_{\max }}-\frac{{p^{\&prime;}}_s}{(s-{\mathrm{\&rho;}}^{\&prime;}-1)(1-{{\mathrm{\&rho;}}^{\&prime;}}_s)}[e^{-{\mathrm{\&mu;}}^{\&prime;}{D^{\&prime;}}_{\max }}-e^{-{\mathrm{\&mu;}}^{\&prime;}(s-{\mathrm{\&rho;}}^{\&prime;}){D^{\&prime;}}_{\max }}],{\mathrm{\&rho;}}^{\&prime;}\&NotEqual;s-1.\end{array}\right.---\left(4\right)$

In formula: R' is the timely reliability of similar network, D' _maxrepresent the maximum delay that user allows, λ ' is the similar network data interval time of advent, the average service time that μ ' is similar network, and service number of units is s;

Make the service number of units s in similar network not change, consider p _s=f (ρ), actual in formula (3) have 4 physical quantitys, i.e. R, λ, μ and D, makes affinity constant be respectively c _r, c _λ, c _μand c _d, represent the change multiple of relevant parameter in parameter and primal system in similar network, that is:

$\left\{\begin{array}{c}{R}^{\&prime;}=c_R\&CenterDot;R\\ {\mathrm{\&mu;}}^{\&prime;}=c_{\mathrm{\&mu;}}\&CenterDot;\mathrm{\&mu;}\\ {\mathrm{\&lambda;}}^{\&prime;}=c_{\mathrm{\&lambda;}}\&CenterDot;\mathrm{\&lambda;}\\ {D^{\&prime;}}_{\max }=c_D\&CenterDot;D_{\mathrm{m\&epsiv;}}\end{array}\right.---\left(5\right)$

If the reliability R in the reliability R' in similar network and primitive network remains unchanged, that is: c _r=1; And it is equal according to the affinity constant of interarrival time and average service time to take the mean, i.e. c _μ=c _λ; According to similar first theorem, simultaneous formula (3), formula (4) and (5), then can obtain: c _μc _d=1;

Thus, obtain 3 similarity criterions of M/M/s queuing model, this criterion is reliability acceleration model:

$\left\{\begin{array}{c}{c}_R=1\\ c_{\mathrm{\&mu;}}=c_{\mathrm{\&lambda;}}\\ c_{\mathrm{\&mu;}}\&CenterDot;c_D=1\end{array}\right.---\left(6\right)$

Along with network data arrives the increase of intensity, the packet number arrived in same time increases, and reliability information amount increases, and network data arrives intensity and increases c _λdoubly, test duration reduces c _λdoubly, the data volume of twice test is constant, and the pass of namely testing duration and network data arrival intensity is:

c _λ＝t/t' (7)

In formula: t is primitive network test duration, t' is similar network test duration;

Step 4: carry out the timely reliability accelerated test of network;

Specifically comprise the steps:

Step 4.1, determines network data collection quantity, and hypothetical network model is M/M/s queuing model, and delay fault obeys binomial distribution, value inspection upper limit R, discrimination ratio D, Production venture α and consumer's risk β; Check in reliability compliance test the Delay quantity requiring at least to need to collect packet;

Step 4.2, obtains accelerated test parameter, if primitive network mission profile parameter and delay threshold are λ, μ and D _max, test duration is t; According to (6) formula rule interestingness λ, μ and D _maxcorresponding similarity factor c _λ, c _μand c _d, obtain λ ', μ ' and D ' _max; Carrying out duration according to accelerated test parameter is t'=t/c _λreliability accelerated test, obtain the timely reliability of this accelerating network; This value thinks identical with the timely reliability of primitive network, namely obtains the timely reliability of primitive network.