CN112099932A - Optimal pricing method and system for soft-hard deadline task offloading in edge computing - Google Patents
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Abstract
The invention discloses an optimal pricing method and an optimal pricing system for soft-hard deadline task unloading in edge calculation, wherein the method comprises the following steps: designing an edge-cloud computing system model, and dividing tasks in the system into high-priority tasks and low-priority tasks; establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps of establishing a queue model for an edge server as an M | M |1 queue, and establishing a queue model for a cloud server as an M | M | ∞ queue; calculating the response time of the hard deadline task and the soft deadline task in the edge server and the cloud server; respectively calculating the cost of the edge server and the cost of the cloud server; respectively calculating the profits of the edge server and the cloud server; modeling the cost of the system using Wardrop; modeling the system revenue by adopting Nash balance; the efficiency of the pricing strategy is evaluated. The invention can find a pricing strategy for balancing cost minimization and income maximization.
Description
Technical Field
The invention relates to an optimal pricing method and system for soft-hard deadline task unloading in edge calculation, and belongs to the technical field of edge calculation.
Background
The edge computing is originated in the field of media, and means that an open platform integrating network, computing, storage and application core capabilities is adopted on one side close to an object or a data source to provide nearest-end service nearby. By extending computing and storage resources to resource-constrained end users, edge computing greatly eliminates the transmission delay bottleneck between end users and remote cloud data centers. However, edge servers are greatly limited in terms of computing and resource storage compared to resource-rich cloud servers. Thus, task processing and computational allocation of resources has been a challenging problem in edge computing systems.
In edge computation, delay-sensitive tasks can be classified according to timeliness constraints: hard deadline tasks and soft deadline tasks. In a general purpose computing environment, many schedulers are proposed in succession. These schedulers have been developed based on the number of tasks missing an expiration date under various time and resource constraints. By taking the similarity and timeliness characteristics of tasks, how to schedule these tasks in a limited computing resource is an interesting research topic in edge computing.
One scheduling strategy is devised in reference 1, namely by selecting the position best suited for hard deadline and soft deadline tasks. Their hard deadline tasks require a very strict deadline to execute in the embedded system. The remaining computing resources of the edge nodes are used to perform soft deadline tasks, causing these tasks to suffer from maximum delays beyond their deadlines. While reference 1 lays a solid foundation for task offloading based on expiration dates, there is little interaction between edges and clouds. Furthermore, they do not take into account computational costs.
Reference 2 discusses the decentralized resource allocation of tasks according to their requirements and the computational model of the network, their main purpose being to reduce the overhead of the system. Reference 3 is studied from the point of view of pricing models and resource allocation of micro-economics theory, aiming at optimizing the limited resources of the terminal device task in edge computing within a limited budget.
To maximize the social benefit of the network, reference 4 suggests using a platform in a business model based on shared economics that can be used to manage network resources in real time. The platform maximizes profit without relying on any user decision as to where to place and process the task.
In summary, pricing models are mainly designed in the literature at present, and an optimal pricing mechanism is designed for a specific network scenario. These pricing models do not explicitly consider deadlines, especially hard and soft deadline tasks in edge calculations. Therefore, the following technical requirements in the prior art need to be solved: how to set prices for different deadline tasks maximizes edge cloud revenue by utilizing its own computing and transmission capabilities.
The references are as follows:
[1]N.Auluck,A.Azim,and K.Fizza,“Improving the schedulability of real-time tasks using fog computing,”IEEE Transactions on ServicesComputing,pp.1–14,Sept.2019.
[2]Q.He,G.Cui,X.Zhang,F.Chen,S.Deng,H.Jin,Y.Li,and Y.Yang,“A game-theoretical approach for user allocation in edge computing environment,”IEEE Trans.Parallel Distrib.Syst.,vol.31,no.3,pp.515–529,Mar.2020.
[3]J.Liu,S.Guo,K.Liu,and L.Feng,“Resource provision and allocation based on microeconomic theory in mobile edge computing,”IEEE Trans.Serv.Comput.,pp.1–14,June 2020,
[4]M.Siew,D.W.H.Cai,L.Li,and T.Q.S.Quek,“Dynamic pricing for resource-quota sharing in multi-access edge computing,”IEEE Trans.Netw.Sci.Eng.,pp.1–13,June 2020。
disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an optimal pricing method and system for soft-hard deadline task offloading in edge computing, so that an edge-cloud computing system can find a pricing strategy for balancing cost minimization and income maximization.
The invention specifically adopts the following technical scheme: the optimal pricing method for soft-hard deadline task unloading in edge calculation comprises the following steps:
step SS 1: designing an edge-cloud computing system model, and dividing tasks in the system into high-priority tasks and low-priority tasks;
step SS 2: establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps of establishing a queue model for an edge server as an M | M |1 queue, and establishing a queue model for a cloud server as an M | M | ∞ queue; calculating the response time of the hard deadline task and the soft deadline task in the edge server and the cloud server;
step SS 3: respectively calculating the cost of the edge server and the cost of the cloud server;
step SS 4: respectively calculating the profits of the edge server and the cloud server;
step SS 5: modeling the cost of the system using Wardrop;
step SS 6: modeling the system revenue by adopting Nash balance;
step SS 7: the efficiency of the pricing strategy is evaluated.
As a preferred embodiment, the division of the tasks in the system in step SS1 is based on the time limit of the tasks; high priority tasks typically require a hard deadline and low priority tasks require a soft deadline, so the tasks are also divided into hard and soft deadline tasks; let λ be the amount of tasks reached:
λ＝λH+λS
wherein λ isHFor the number of hard deadline tasks, λSIs the number of soft deadline tasks.
As a preferred embodiment, step SS2 specifically includes:
the number of hard deadline tasks includes the number of hard deadline tasks in the edge server
And the number of hard deadline tasks in the cloud server
Similarly, the number of soft deadline tasks includes the number of soft deadline tasks in the edge server
And the number of soft deadline tasks in the cloud server
Then there are:
the response time of the hard deadline task on the edge server and the cloud server is respectively as follows:
the response time of the soft deadline task on the edge server and the cloud server is respectively as follows:
wherein, muEAnd muCThe service rates are the number of tasks completed by the server in a unit time.
As a preferred embodiment, step SS3 specifically includes:
the cost of hard deadline tasks in edge servers is:
the soft deadline task cost in the edge server is:
where α is a parameter used to balance the relationship between delay and cost, i.e., the longer the task processing time, the higher the total cost; pECost for each task on the edge server;
the costs of hard deadline tasks and soft deadline tasks in a cloud server are as follows:
wherein d istAverage transmission delay for transferring a single task from an edge server to a cloud server, PCFor the cost of each task on the cloud server.
As a preferred embodiment, step SS4 specifically includes:
the edge server gains are:
the yield of the cloud server is as follows:
As a preferred embodiment, step SS5 specifically includes:
the total cost of the soft and hard deadline tasks in the balance is equal, namely:
the proportion of the soft deadline tasks in the total tasks plays an important role in the overall cost of computing the total cost of the cloud server and the edge server, and is therefore written as follows:
where φ is the offset of the expiration date.
As a preferred embodiment, step SS6 specifically includes:
definition of
And
nash prices for edge servers and cloud servers, respectively, wherein
The definition is as follows:
in the same way, the method for preparing the composite material,
the definition is as follows:
wherein
γ＝2(λ-2μE)2，
As a preferred embodiment, step SS7 specifically includes:
in order to evaluate the efficiency of the pricing strategy, a price-of-annular strategy POA is introduced; a social welfare function S is defined,
wherein x and y are hard deadline and right deadline tasks, respectively;
minimizing the social welfare function S, the above formula is rewritten as follows:
wherein, T*Is the total delay experienced in the network in the equilibrium state.
As a preferred embodiment, step SS7 further includes: POA according to T*And SminAnd (3) calculating: POA ═ T8/Smin。
The invention also provides an optimal pricing system for soft-hard deadline task offloading in edge computing, which comprises the following steps:
a task partitioning module to perform: designing an edge-cloud computing system model, and dividing tasks in the system into high-priority tasks and low-priority tasks;
a queue model generation module to perform: establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps of establishing a queue model for an edge server as an M | M |1 queue, and establishing a queue model for a cloud server as an M | M | ∞ queue; calculating the response time of the hard deadline task and the soft deadline task in the edge server and the cloud server;
a server cost calculation module to perform: respectively calculating the cost of the edge server and the cost of the cloud server;
a server revenue calculation module to perform: respectively calculating the profits of the edge server and the cloud server;
a system cost modeling module to perform: modeling the cost of the system using Wardrop;
a system revenue modeling module to perform: modeling the system revenue by adopting Nash balance;
an efficiency evaluation module to perform: the efficiency of the pricing strategy is evaluated.
The invention achieves the following beneficial effects: the invention provides an optimal pricing method for soft-hard deadline task unloading in edge calculation. The method comprises the steps of determining the balanced price of an edge server and a cloud server by designing a pricing model, firstly constructing an edge-cloud server system, dividing tasks of soft and hard deadlines, then establishing an edge server and cloud server queue model to determine the response time of the soft and hard deadlines, then designing cost and gain functions of the edge server and the cloud server, and finally modeling the cost and the gain of the system by adopting Nash balance and Wardrop balance, so that the system can find a pricing strategy for minimizing the balanced cost and maximizing the gain.
Drawings
FIG. 1 is a schematic diagram of an edge-cloud computing system model of the present invention;
FIG. 2 is a schematic diagram of the hard deadline task and the soft deadline task of the present invention;
fig. 3 is a schematic diagram of the soft and hard deadline tasks of the present invention being processed locally in the edge server or offloaded to the cloud server.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1: as shown in fig. 1, fig. 2 and fig. 3, an edge-computed optimal pricing method for hard-soft deadline task offloading of the present invention comprises the following seven steps.
1) An edge-cloud computing system model is designed, as shown in fig. 1, and the tasks in the system are divided into high-priority and low-priority tasks.
The edge-cloud server system provided by the invention is assumed to be a time slot system and can be divided into a high-priority task and a low-priority task according to task priorities. And can be divided into hard deadline tasks and soft deadline tasks according to different time requirements of the tasks. Wherein the high priority tasks correspond to hard deadline tasks for ensuring correct operation of the system. Soft deadline tasks may tolerate longer delays than hard deadline tasks. As shown in fig. 2, the soft deadline task is one more offset in delay than the hard deadline task. Let λ be the amount of tasks that the system arrives at, which consists of hard deadline task amount and soft deadline task amount:
λ＝λH+λS
wherein λ isHFor the number of hard deadline tasks, λSIs the number of soft deadline tasks.
2) And establishing a queue model, respectively establishing the queue model for the edge server and the cloud server, and calculating the response time of the hard and soft deadline task in the edge server and the cloud server respectively.
Without loss of generality, the invention models the edge server as an M | M |1 queue and the cloud server as an M | M | ∞ queue. Definition of muEAnd muCThe service rates are the number of tasks completed by the server in a unit time. The number of hard deadline tasks is determined by the number of hard deadline tasks in the edge server
And the number of hard deadline tasks in the cloud server
Similarly, the number of soft deadline tasks is determined by the number of soft deadline tasks in the edge server
And the number of soft deadline tasks in the cloud server
The response time of the hard deadline task on the edge server and the cloud server is respectively
And
the response time of the soft deadline task on the edge server and the cloud server is respectively
And
3) respectively calculating the cost of the edge server and the cloud server:
3.1 Soft and hard deadline task cost in edge servers
In order to better balance the relationship between delay and cost, the present invention introduces a parameter α, i.e. the longer the task processing time, the higher the total cost spent.
The total cost of the hard deadline task is calculated as follows:
wherein P isEThe cost required to process one task for the edge server.
The total cost of the soft deadline task is calculated as follows:
3.2 software and hardware deadline task cost in cloud Server
The total cost of the hard deadline task is calculated as follows:
the total cost of the soft deadline task is calculated as follows:
wherein d istAverage transmission delay for transferring a single task from an edge server to a cloud server, PCFor the cost of each task on the cloud server.
4) Revenue of edge server and cloud server:
edge server revenue UEThe definition is as follows:
cloud server profit UCThe definition is as follows:
5) the overall cost of the system is modeled with Wardrop balancing:
the total cost of soft and hard deadline tasks in Wardrop balancing is equal-that is
The proportion of the soft deadline tasks in the total tasks plays an important role in the overall cost of computing the total cost of the cloud server and the edge server, and can therefore be written as follows:
where φ is the offset of the expiration date.
6) Nash equilibrium is employed to model the overall revenue of the system:
nash equilibrium is used for modeling the total benefit of the system, and the system is strived to obtain the maximum benefit. We define
And
nash prices for edge servers and cloud servers, respectively, wherein
Is defined as follows
Wherein
γ＝2(λ-2μE)2,
And
in the same way, the method for preparing the composite material,
the definition is as follows:
7) evaluating the efficiency of the pricing strategy:
in order to better evaluate the efficiency of the pricing strategy, the invention introduces a price-of-annuity (POA) strategy. A social welfare function S is defined,
where x and y are hard deadline and soft deadline tasks, respectively.
In order to minimize the social welfare function S, the above formula is rewritten as follows:
further, the total delay experienced in the network in the equilibrium state is defined as follows:
finally, the POA policy may be based on T*And SminAnd (3) calculating: POA ═ T*/Smin。
Example 2: the invention also provides an optimal pricing system for soft-hard deadline task offloading in edge computing, which comprises the following steps:
a task partitioning module to perform: designing an edge-cloud computing system model, and dividing tasks in the system into high-priority tasks and low-priority tasks;
a queue model generation module to perform: establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps of establishing a queue model for an edge server as an M | M |1 queue, and establishing a queue model for a cloud server as an M | M | ∞ queue; calculating the response time of the hard deadline task and the soft deadline task in the edge server and the cloud server;
a server cost calculation module to perform: respectively calculating the cost of the edge server and the cost of the cloud server;
a server revenue calculation module to perform: respectively calculating the profits of the edge server and the cloud server;
a system cost modeling module to perform: modeling the cost of the system using Wardrop;
a system revenue modeling module to perform: modeling the system revenue by adopting Nash balance;
an efficiency evaluation module to perform: the efficiency of the pricing strategy is evaluated.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. The optimal pricing method for soft-hard deadline task offloading in edge computing is characterized by comprising the following steps of:
step SS 1: designing an edge-cloud computing system, wherein the edge-cloud computing system comprises an edge server and a cloud server, and tasks entering the system are divided into high-priority tasks and low-priority tasks according to cut-off;
step SS 2: establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps that a queue model is established for an edge server to be an M | M |1 queue, a queue model is established for a cloud server to be an M | M | ∞ queue, 1 represents that only 1 server exists, and infinity represents that an infinite server exists; calculating the response time of the hard deadline task and the soft deadline task in the edge server and the cloud server;
step SS 3: respectively calculating the cost of the edge server and the cost of the cloud server;
step SS 4: respectively calculating the profits of the edge server and the cloud server;
step SS 5: modeling the cost of the system using Wardrop;
step SS 6: modeling the system revenue by adopting Nash balance;
step SS 7: the efficiency of the pricing strategy is evaluated.
2. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 1, wherein the division of tasks in the system in step SS1 is based on time deadline of task; high priority tasks typically require a hard deadline and low priority tasks require a soft deadline, so the tasks are also divided into hard and soft deadline tasks; let λ be the amount of tasks reached:
λ＝λH+λS
wherein λ isHFor the number of hard deadline tasks, λSIs the number of soft deadline tasks.
3. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 2, wherein the step SS2 specifically comprises:
the number of hard deadline tasks includes the number of hard deadline tasks in the edge server
And the number of hard deadline tasks in the cloud server
Similarly, the number of soft deadline tasks includes the number of soft deadline tasks in the edge server
And the number of soft deadline tasks in the cloud server
Then there are:
the response time of the hard deadline task on the edge server and the cloud server is respectively as follows:
the response time of the soft deadline task on the edge server and the cloud server is respectively as follows:
wherein, muEAnd muCThe normalized service rates of the edge server and the cloud server are respectively, that is, the number of tasks completed by the edge server and the cloud server in unit time.
4. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 3, wherein said step SS3 specifically comprises:
the cost of hard deadline tasks in edge servers is:
the soft deadline task cost in the edge server is:
where α is a parameter used to balance the relationship between delay and cost, i.e., the longer the task processing time, the higher the total cost; pECost for a single task on an edge server;
the costs of hard deadline tasks and soft deadline tasks in a cloud server are as follows:
wherein d istAverage transmission delay for transferring a single task from an edge server to a cloud server, PCThe cost of a single task on the cloud server.
5. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 4, wherein the step SS4 specifically comprises:
the edge server gains are:
the yield of the cloud server is as follows:
6. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 5, wherein the step SS5 specifically comprises:
the total cost of the soft and hard deadline tasks in the balance is equal, namely:
the role played by the proportion of the total tasks in the cloud server and edge server computing the total cost based on the soft deadline tasks is therefore written as follows:
wherein,
representing the cost of the soft deadline task at the edge server,
representing the cost of the soft deadline task at the cloud server, alpha > 0 is a parameter for balancing the relation between the delay and the cost, and lambdaSDenotes the number of soft deadline tasks to arrive at the system, λ denotes the total number of tasks to arrive at the system, is the sum of the number of soft deadline tasks and the number of hard deadline tasks, μCRepresents the service rate, mu, of the cloud serverERepresents the service rate of the edge server and phi is the offset of the expiration date.
7. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 6, wherein said step SS6 specifically comprises:
definition of
And
nash prices for edge servers and cloud servers, respectively, wherein
The definition is as follows:
in the same way, the method for preparing the composite material,
the definition is as follows:
wherein
γ＝2(λ-2μE)2，
The meaning of k.
8. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 7, wherein the step SS7 specifically comprises:
in order to evaluate the efficiency of the pricing strategy, a price-of-annular strategy POA is introduced; a social welfare function S is defined,
wherein x and y are hard deadline and right deadline tasks, respectively;
minimizing the social welfare function S, the above formula is rewritten as follows:
wherein, T*The meaning of d is the total delay experienced in the network in equilibrium.
9. The optimal pricing method for soft-hard deadline task offloading in edge computing according to claim 8, wherein the step SS7 further comprises: POA according to T*And SminAnd (3) calculating: POA ═ T*/Smin。
10. An optimal pricing system for soft-hard deadline task offloading in edge computing, comprising:
a task partitioning module to perform: designing an edge-cloud computing system model, and dividing tasks in the system into high-priority tasks and low-priority tasks;
a queue model generation module to perform: establishing a queue model, and respectively establishing the queue model for the edge server and the cloud server; the method comprises the following steps of establishing a queue model for an edge server as an M | M |1 queue, and establishing a queue model for a cloud server as an M | M | ∞ queue; calculating response time of the hard deadline task and the soft deadline task in the edge server and the cloud server;
a server cost calculation module to perform: respectively calculating the cost of the edge server and the cost of the cloud server;
a server revenue calculation module to perform: respectively calculating the profits of the edge server and the cloud server;
a system cost modeling module to perform: modeling the cost of the system using Wardrop;
a system revenue modeling module to perform: modeling the system revenue by adopting Nash balance;
an efficiency evaluation module to perform: the efficiency of the pricing strategy is evaluated.
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