School of CIE, Chongqing University of Posts and Telecommunications, Chongqing, China 400065. â ... A cloud service provisioning model generally consists of.
A New Economic Model in Cloud Computing: Cloud Service Provider vs. Network Service Provider Jun Huang∗ , Fang Fang∗ , Yi Sun∗ , Huifang Yan∗ , Cong-cong Xing† , Qiang Duan‡ , Wei Wang§ ∗ School
of CIE, Chongqing University of Posts and Telecommunications, Chongqing, China 400065. of Mathematics and Computer Science, Nicholls State University, Thibodaux, LA 70310. ‡ IST Department, The Pennsylvania State University, Abington, Pennsylvania 19001. § CS Department, San Diego State University, Campanile Drive, USA 92115.
† Department
Abstract—Cloud computing has emerged as a new computing paradigm and its economics has opened up a new research area. Though progress has been made toward address competitions among Cloud service providers (CSPs) or among network service providers (NSPs), few studies have focused on the relationship between CSPs and NSPs. In this paper, we investigate this problem and present a new economic model to characterize the competition between CSPs and NSPs. We then conduct thorough theoretical analysis and numeric experiments to validate the proposed model. The results show that the replacement coefficient, connection rate, service coefficient, the equilibrium will affect the market share and the profit of CSPs and NSPs. Through this study, we believe that the developed economic model is general and practical, thus it is applicable to model the Cloud computing market.
I.
I NTRODUCTION
Cloud computing is a recent emerged paradigm in the information technology field that reshapes the way of service management and provisioning. Cloud computing is driven by economies of scale, in which a pool of abstracted, virtualized, dynamically scalable computing functions and services are delivered on demand to external customers over the Internet [1]. A cloud service provisioning model generally consists of three types of participants [2]: cloud service provider (CSP), network service provider (NSP), and end user, where CSPs are the suppliers of cloud services, NSPs provide network transport or access service for both CSPs and end users, and end users are consumers of cloud and network services. In a rough sense, end users submit service requests to CSPs via NSPs, while CSPs lease infrastructures from NSPs and deliver back requested services to end users. With this model, customers are able to obtain the cloud services on a “pay-as-you-go” basis. In the cloud service provisioning, CSP and NSP are usually supposed to be co-dependent. The revenue of NSPs mainly come from CSPs and end users who use networking services, and thus NSPs would receive higher profit if CSPs gain more share in cloud computing market. With the expansion of cloud market, the relationship between CSP and NSP, however, is changing profoundly. In addition to providing network services, NSPs start offering cloud services to end users as well. For example, Verizon has released Verizon Cloud that provides IaaS-based storage services [3]. Compared with the same storage services offered by Amazon or Rackspace, Verizon Cloud storage services can guarantee the network performance to the customers much easier through their own Verizon networks. This sort of change leads to a new cloud
market trend and even more complicated interactions between CSPs and NSPs. When CSPs and NSPs provide substitutable Cloud services such as storage or computing, NSPs, on one hand, may gain higher revenue if CSPs take more cloud storage market share, that is, NSPs derive higher profit as CSPs and end users use more network services. On the other hand, NSPs may lose revenue due to competition with CSPs providing the same cloud services. From CSPs’ perspective, they not only cooperate with NSPs for service delivery, but also compete with NSPs for more cloud market share. Therefore, interactions and competition between CSPs and NSPs play a vital role in cloud computing market size, which calls for a new economic model to characterize such relationship. Network economics has become an active research area, but it is still in its infancy in the context of cloud computing. Feng et al. [4] studied price competition in a cloud market formed by multiple IaaS cloud providers, and provided an analytical study on the monopoly, duopoly, and oligopoly markets where multiple IaaS cloud providers are competing with one another. Roh et al. [5] formulated a resource pricing problem in geo-distributed clouds by considering the game between CSP and application service provider (ASP), where the ASP acts as the CSP agent who provides cloud services without constructing its own private data centers. Pueschel et al. [6] developed models that are capable of predicting revenue and utilization achieved with admission-control policy based revenue management under stochastic demand, which allows CSP to significantly increase revenue by choosing the optimum policy. Petri et al. [7] studied the effects of risk in service-level agreements (SLAs) in service provider communities. Allon and Federgruen [8] examined the scenario that multiple providers competed for users using different prices and time guarantees. The competition game among multiple resource providers was also considered in networking research. Existing works have considered competitions either among CSPs or among NSPs, few studies have focused on the relationship between CSPs and NSPs. Zhang et al. [9] modeled the competition between service providers using Cournot games, and the competition between network providers using Bertrand games, then these two types of games were tied together in a two-stage Stackelberg game. Though this is the first attempt to address the relationship between service providers and network providers, competitions between them when network service providers offer the same service with service providers are not characterized in the context of cloud computing.
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In this paper, we use Game Theory to model the competition between CSPs and NSPs, analyze the factors that will affect the market share and the profit of CSPs and NSPs, and investigate the ensuing Nash Equilibrium in the competition. The contributions of this work are summarized as follows. •
We investigate the competition between CSPs and NSPs and formally present a game-theoretic model, in which the payoff of a service provider is defined by the proportional to its market share and its utility.
•
We conduct extensive theoretical analysis and numeric experiments to determine the factors such as replacement coefficient, connection rate, service coefficient, the equilibrium that will affect the market share and the profit of CSPs and NSPs. Interestingly, we find that: 1) service provider with a small substitutable probability has a competitive edge and a relatively high profit. 2) A high connection rate may result in a service provide would need to spend more on improving its customer service quality. 3) A larger service capability would lead to a service provider’s market share and profit depend more on its service rate. 4) The equilibrium point would increase when the service coefficient decreases, or the connection rate decreases, or the replacement coefficient increases. We believe that the proposed economic model is general and practical, thus it is applicable to characterize Cloud computing market.
The rest of the paper is organized as follows. Section II presents the system model of the competition using Game Theory, and section III addresses the issue of Nash Equilibrium among competitors. Experiments are conducted in Section IV to demonstrate correlations among various factors in the competition, and Section V concludes the paper. II.
S YSTEM M ODEL
In this section, we describe the model of the system and make the following assumptions throughout the paper: •
There are only two types of service providers on the cloud service market: CSPs that only offer cloud services, and NSPs that offer both cloud services and network services.
•
Each user can only choose one service provider: either an CSP or an NSP.
•
Service providers can always satisfy the marketing demands.
•
The Cloud services offered by CSPs and NSPs are of the same quality.
•
There exists a minimum value in terms of user utility. If the service provided to a user by a service provider fails to generate a user utility larger than or equal to this minimum value, then the user will not choose this service provider.
Both CSPs and NSPs are configured with an M/M/1 queue, serving a common pool of potential cloud users with one “super” server. We use uti to denote the service rate (i.e., the ability of a service provider to deal with users’ requests) of
the service provider i (an CSP or NSP). Note that the service rate of a service provider relies on its resource capacity; a stronger resource capacity would certainly lead to a higher service rate, that is, the service rate of a CSP and that of a NSP are different. Considering the randomness of the users’ service requests arrivals in cloud service systems and the characteristics of cloud service delivery, the arrival rate of user requests can be generally regarded as a Poisson distribution [10], [11]. For a user j, we use λj to represent the amount of information that needs to be processed for. Assuming the number of users is M , then the sum of all users’ service request equal to the total cloud service market size, that is Λ = j λj (j = 1, 2, · · · , M ). Let μtc , μtn be the service rate of CSP and NSP in the k-th round of the competition respectively, then by [4], the service time of the CSP and the service time of the NSP in the k-th round of the competition would be λ tck = q·μjt c , (1) λ tnk = q·μjt n
where q is the connection rate indicting the probability of users’ service requests being successfully processed by the service provider. Note that the connection rate depends on the quality and availability of the communication network infrastructure – a higher quality communication network infrastructure will give rise to a higher connection rate, and that CSPs need to use the network facilities provided by NSPs to serve the users. We assume, without loss of generality, that the connection rates offered by CSPs and NSPs are equal. The experience values Qck and Qnk of a cloud service user with an CSP or an NSP, in the k-th round of the competition, can be calculated as follows c Qk (λj ) = gλj − ptck , (2) Qnk (λj ) = gλj − ptnk where g(g > 0) is the benefit factor of the user utility and p(p > 0) is the time cost factor of the user utility. Note that formula (2) reveals the fact that the experience value of a user with a service provider is closely related to the service time; a shorter service time means a higher service efficiency and a higher user experience value. Also, since it has been assumed that service providers can always satisfy the marketing demands, we have μ > f for any service provider. A service provider will charge a user for the service it provides. If the price that a service provider charges its users, in the k-th round of the competition, is P , and the service request amount of user is λj , then the fee that user needs to pay would be P λj . For user, we define its user utility Uki (λj ) when being served by service provider i, in the k-th round of the competition, to be Uki (λj ) = Qik (λj ) − Pki · λj .
(3)
It is worth noting that a larger value of Uki (λj ) indicates user j has a stronger desire of choosing service provider i (as opposed of choosing other service providers). Instantiating in formula (3) by a specific service provider (CSP or NSP) results in the following c Uk (λj ) = Qck (λj ) − Pkc · λj . (4) Ukn (λj ) = Qnk (λj ) − Pkn · λj
Users are an indispensable part of the cloud service market. User utility is the direct indication of the competence of a service provider in the market in the sense that a higher user utility for a service provider would likely attract more users to this service provider. In our work, we assume that the minimum expected value for the user utility is v. If user utility lower than v, then user would choose to be served by other service providers rather than current service provider. Thus, the condition for user to choose service provider to do business is Uki (λj ) = gλj −
pλj − Pki · λj ≥ v. q · μti
(5)
Price plays an important role in competition of service providers, and alterations of price may affect user utilities and thus the market share of service providers. It can be derived from formula (5) that when the price of service provider i is Pki , the service rate uti satisfies the following condition p (6) ≤ μti , v q[g − Pki − M ] ft i
which suggests that if the service rate of service provider in the k-th round of the competition not meets the formula (6), then this service provider will no longer be able to meet the demands of users and will be rejected by the users. In the cloud service market, the operational cost of one service provider is likely to be different from that of another service provider due to their individual ways of running business. We use cck (utc ) and cnk (utn ) to represent the operational cost of an CSP and an NSP in the k-th round of the competition, and compute them as follows c t ck (uc ) = k1c μtc + k2c q , (7) cnk (utn ) = k1n μtn + k2n q where k1c and k1n denote the cost of the CSP and the NSP on the service quality respectively, k2c and k2n denote the cost of the CSP and the NSP on network maintenances. Clearly, a larger value of the service rate μti or the connectivity rate q would mean that the service provider needs to spend more on the quality guarantee of customer service, which inevitably will increase the operational costs. Moreover, since an CSP typically needs to rent the networking facilities from an NSP in order to provide cloud services to its customers, it is reasonable to have k2c > k2n . Based on the analyses above, we can calculate the utility Ukc (utc ) of an CSP and the utility Ukn (utn ) of an NSP in the k-th round of the competition as follows c t Uk (uc ) = Pkc − cck (utc ) , (8) Ukn (utn ) = Pkn − cnk (utn ) which can be rewritten as c t Uk (uc ) = Pkc − k1c μtc − k2c q . Ukn (utn ) = Pkn − k1n μtn − k2n q
(9)
Formula (9) clearly indicates that a larger value of service rate μti or a larger value of connection rate q of service providers would decrease the utility of service providers. This makes sense because a larger μti or q suggests that the service providers need to increase the operational costs to improve its customer service quality, and as a result, the user utility
would be increased and the service provider utility would be decreased at the same. The profits πct and πnt of an CSP and an NSP in the k-th round of the competition are defined as follows t πc = fct · Ukc (utc ) , (10) πnt = fnt · Ukn (utn ) where fct and fnt are the market shares of the CSP and the NSP respectively. It can be seen that the profit of a service provider is decided by and proportional to its market share and its utility. III.
C OMPETITION A MONG S ERVICE P ROVIDERS
The competition among service providers can be seen from the fact that if the user’s utility that an user receives from a service provider is lower than the minimum expected value, then the user would reject this service provider and select another service provider. So each service provider will try to lower its price to attract more users resulting in a price war among service providers. However, the competition will eventually come to an end with an equilibrium. Considering that during the competition, each service provider always pursues its utility and profit maximization, we may model this competition as a non-cooperative game. In the discussion and analysis below, we assume that there are total n(n ≥ 2) service providers on the market with m (0 < m < n) CSPs and (n−m) NSPs. We know that service quality of a service provider is proportional to its market demands. That is, a superior service quality will lead to a higher demand in the market. Also, we notice that the cloud service provided by an CSP can be replaced by that provided by an NSP, and vice versa. Specifically, the cloud service provided by an CSP or an NSP can be replaced by the cloud service provided by another CSP or another NSP. Thus ⎧ m n−m ⎪ 1 1 i ⎪ f = a u − u − b1j ujn 1 ⎪ c c c ⎪ ⎪ j=1 i=1,i=1 ⎪ ⎪ m n−m ⎪ ⎪ ⎪ ⎪ fcm = am um − uic − bmj ujn c ⎪ ⎪ ⎪ j=1 i=1,i = m ⎪ ⎪ ⎪ .. ⎨ . (11) n−m m ⎪ 1 1 j ∗ i ⎪ = a u − u − b u f ⎪ m+1 n n n ⎪ (m+1)i c ⎪ i=1 j=1,j=1 ⎪ ⎪ ⎪ ⎪ ⎪ .. ⎪ . ⎪ ⎪ ⎪ n−m m ⎪ ⎪ ⎪ − ujn − b∗ni uic ⎩ fnn−m = an un−m n j=1,j=n−m
i=1
where i ∈ {1, · · · , m} j ∈ {1, · · · , n − m}, bij is the replacement coefficient of CSP with respect to NSP which indicates the probability that an CSP i can be replaced by an NSP j; similarly, b∗(m+j)i is the replacement coefficient of NSP with respect to the CSP which indicates the probability that an NSP j can be replaced by an CSP i. Each service provider has its maket dominance, so bij , b∗(m+j)i ∈ (0, 1). A larger replacement coefficient of a service provider indicates a stronger possibility that this service provider will be replaced by another one; in other words, its market share is more easily affected by other service providers. a1 , · · · , an are service
11
0.2
b =...=b 11
=0.8
0.15
1(n−m)
π1c
f1c
b11=...=b1(n−m)=0.7
0.6
b =...=b 11
=0.6
1(n−m)
0.6
=0.5
1(n−m)
b11=...=b1(n−m)=0.6
0.5
b11=...=b1(n−m)=0.7 b =...=b 11
=0.8
1(n−m)
0.1
0.4
0.75
0.8
0.85
0.9
1
0.95
0
1
2
3
m
1
n−m
uc +uc +...+uc =1.8,un=...=un
2
0.4
=0.6
m
1
n−m
=0.6
u2c+u3c+...+um =1.8,u1n=...=un−m =0.7 c n
u2c+u3c+...+um =1.8,u1n=...=un−m =0.8 c n
1.2
0.4
3
uc +uc +...+uc =1.8,un=...=un
u2c+u3c+...+um =1.8,u1n=...=un−m =0.7 c n
u2c+u3c+...+um =1.8,u1n=...=un−m =0.8 c n
0.3
u2c+u3c+...+um =1.8,u1n=...=un−m =0.9 c n
u2c+u3c+...+um =1.8,u1n=...=un−m =0.9 c n
1 0.2
0.3
0.05
0.2
1.4
q=0.5 q=0.6 q=0.7 q=0.8
π1c
b =...=b
f1c
0.25
b11=...=b1(n−m)=0.5
π1c
0.8
0.8 0.7
0.8
0.9
0.2 0.8
1
0.85
0.9
u1c
uc
(a)
0.95
1
0.8
0.85
u1c
(b)
0.9
0.95
0.1
1
0.6
0.7
0.8
u1c
(c)
0.9
1
u1c
(d)
(e)
Fig. 1. Correlations between b, q, u1n and fc1 , πc1 . (a) Correlation between replacement coefficient and CSP 1’s market share. (b) Correlation between replacement coefficient and CSP 1’s profit. (c) Correlation between connection rate and CSP 1’s profit. (d) Correlation between NSP 1’s service rate and CSP 1’s market share. (e) Correlation between NSP 1’s service rate and CSP 1’s profit.
*
*
0.5
*
0.3
*
π1n
f1n
b11=...=b1(n−m)=0.7
0.6
*
*
*
*
0.5
b11=...=b1(n−m)=0.5
0.4
b11=...=b1(n−m)=0.8
b11=...=b1(n−m)=0.6 b*11=...=b*1(n−m)=0.7 *
0.4
*
q=0.5 q=0.6 q=0.7 q=0.8
b11=...=b1(n−m)=0.8
0.8
2
un+un+...+un
1.4
0.2
1.3
0.8
0.9
1
0.8
1
0.9
1
0.2
0.85
0.9
0.95
1
0.6
1.1
0.9
0.95
1
un
(a)
u2n+u3n+...+un−m =1.5,u1c=...=um =0.9 n c
0.65
1
un
u2n+u3n+...+un−m =1.5,u1c=...=um =0.8 n c
0.7
1.2
0.1 0 0.7
u2n+u3n+...+un−m =1.5,u1c=...=um =0.7 n c
0.75
0.3
0.4 0.2
3 n−m 1 m =1.5,uc =...=uc =0.6 3 n−m 1 m =1.5,uc =...=uc =0.7 2 3 n−m 1 un+un+...+un =1.5,uc =...=um =0.8 c 2 3 n−m 1 un+un+...+un =1.5,uc =...=um =0.9 c
u2n+u3n+...+un−m =1.5,u1c=...=um =0.6 n c
2
un+un+...+un
1.5
π1n
*
f1n
*
*
b11=...=b1(n−m)=0.6
π1n
*
b11=...=b1(n−m)=0.5
0.8
1
0.8
0.85
1
un
(b)
0.55
(c)
0.9
0.95
1
1
un
un
(d)
(e)
1 . (a) Correlation between replacement coefficient and NSP 1’s market share. (b) Correlation between Fig. 2. Correlations between b∗ , q, u1c and fn1 , πn replacement coefficient and NSP 1’s profit. (c) Correlation between connection rate and NSP 1’s profit. (d) Correlation between CSP 1’s service rate and NSP 1’s market share. (e) Correlation between CSP 1’s service rate and NSP 1’s profit.
coefficients of the service providers indicating the correlation between service rate of a service provider and its market share. Based on the result we have so far, the profits of CSPs and NSPs can be showed in formula (12). ⎧ 1 1 1 n−m πc (uc · · · um ) = fc1 · Ukc (u1c ) c , un ...un ⎪ ⎪ ⎪ . ⎪ . ⎪ ⎪ . ⎪ ⎨ m 1 1 n−m πc (uc · · · um ) = fcm · Ukc (um c , un ...un c ) (12) 1 1 m 1 n−m 1 n 1 (u · · · u , u ...u ) = f · U (u π ⎪ c n n n n) k ⎪ ⎪ .n c ⎪ ⎪ . ⎪ ⎪ ⎩ . n−m 1 1 n−m ) = fnn−m · Ukn (un−m ) πn (uc · · · um c , un ...un n Thus, the maximization of profits for service providers, i.e. the equilibrium can be obtained by solving ⎧ 1 n−m max[πc1 (u1c · · · um )] c , un ...un ⎪ ⎪ ⎪ . ⎪ . ⎪ ⎪ . ⎪ ⎨ 1 n−m )] max[πcm (u1c · · · um c , un ...un . (13) 1 1 m 1 n−m (u · · · u , u ...u )] max[π ⎪ n c c n n ⎪ ⎪ ⎪ .. ⎪ ⎪ ⎪ ⎩ . 1 n−m max[πnn−m (u1c · · · um )] c , un ...un
Then the solution of the system of equations (14) would be the Nash Equilibrium of the competition among service providers. IV.
E XPERIMENTAL R ESULT
In this section, we investigate the internal correlations between various properties of service providers based on the model established in the previous section. A. Replacement coefficients, connection rates, service rates, market shares, and profits. We first investigate the impacts of replacement coefficients, connection rates and service rates upon the market shares and profits of service providers. Without loss of generality, we use CSP 1 and NSP 1 to typify our study. 1) Correlations between b, q, u1n and fc1 , πc1 : For the sake of computational convenience, data used in the experiments are uniformed and simplified. By letting a = 3.5, Pkc = 1.5, k1c = 0.5, k2c = 0.7, the correlations between replacement coefficient, connection rate, service rate of NSP 1 and market share for CSP 1, profit for CSP 1 are depicted in Fig. 1.
Towards finding a solution for (13), we set
k
ft i
1.2
a =0.55, q=0.7
1.1
a =0.75, q=0.7
1
1
1.1
2
a1=0.65, q=0.7
1
a =0.85, q=0.7
0.9
a1=0.75, q=0.7
0.8
2
a =0.95, q=0.7 2
0.8
(14)
uc
0.9
a1=0.6,q=0.6, a =0.8,q=0.6 2
a1=0.6,q=0.65 a =0.8, q=0.65 2
2
u2c
⎧ ∂π1 (u1 ···um ,u1 ...un−m ) c c c n n ⎪ =0 ⎪ ∂u1c ⎪ ⎪ ⎪ . ⎪ .. ⎪ ⎪ ⎪ ⎪ 1 n−m ⎪ ∂πcm (u1c ···um ) ⎪ c ,un ...un ⎪ =0 ⎪ ∂um c ⎨ 1 1 m 1 n−m ∂πn (uc ···uc ,un ...un ) =0 . ∂u1n ⎪ ⎪ . ⎪ ⎪ .. ⎪ ⎪ ⎪ n−m 1 n−m ⎪ ∂πn (u1c ···um ) ⎪ c ,un ...un ⎪ =0 n−m ⎪ ⎪ ∂u n ⎪ p t ⎪ ⎩ [g−P i − M v ]q ≤ μi
0.7
0.7
a =0.6, q=0.7 1
a2=0.8, q=0.7
0.6
0.6
0.5 0.4
0.6
0.8
1
0.4
0.5
0.6
(a)
0.7
0.8
u1c
u1c
(b)
Fig. 3. Correlation between the service coefficient a, q and Nash equilibrium.
a =0.55, b =0.7,q=0.8 11
0.9
*
=0.85, b*
a
m+1
0.8
=0.55,q=0.8
0.95,
m+1
u1n
u1n
1
a
1
am+1=0.65, b*
b*m+1=0.55,q=0.8
*
am+1=0.65,
* b =0.55,q=0.7 m+1
0.3
0.4
0.5
0.3
a =0.65, b =0.7,q=0.8 1
0.6
a
11
=0.55,
m+1
b*m+1=0.75,q=0.8
0.5 0.4 0.4
0.5
1
(a)
0.6
0.7
0.8
0.2
0.3
0.4
0.5
1
uc
0.6
0.7
1
uc
uc
(b)
(c)
Correlation between the service coefficient a, q, replacement coefficient and Nash equilibrium.
2) Correlations between b∗ , q, u1c and fn1 , πn1 : By letting am+1 = 3.3, Pkn = 1.2, k1n = 0.5, k2n = 0.3, we depict the correlation between replacement coefficient, connection rate, service rate of CSP 1 and market share for NSP 1, profit for NSP 1 in Fig. 2. Fig. 2(a) and 2(b) reveal the correlation between the replacement coefficient and the market share as well as the profit of NSP 1, when q = 0.7, u2n + · · · + un−m = 1.5, u1c + · · · + n m uc = 1.8; Fig. 2(c) shows the correlation between connection rate and the profit of NSP 1 when b∗11 = · · · = b∗1(n−m) = 0.5 = 1.5, u1c + · · · + um and u2n + · · · + un−m n c = 1.8; and Fig. 2(d) and 2(e) exhibit the impact of the service rate of CSP 1 on the market share as well as the profit of NSP 1. Just like the case of CSP 1, we can see that the both the market share and the profit of NSP 1 decrease as the replacement coefficient increases, and that the profit of NSP 1 drops as its connection rate goes up. Also in a similar (reversed) fashion to the case of CSP 1, Fig. 2(d) and 2(e) demonstrate that a larger value of the service rate of CSP 1 will result in lower value of both market share and profit of NSP 1.
0.7
am+1=0.55,q=0.8 a
0.65 0.6
a
a
=0.85,q=0.8
m+2
a
2
=0.95,q=0.8
am+1=0.6,q=0.65 a
=0.8,q=0.65
m+2
1.1
am+1=0.6,q=0.7 a
1
m+2
0.5
=0.8,q=0.6
m+2
1.2
am+1=0.75,q=0.8
0.55
am+1=0.6,q=0.6,
1.3
=0.75,q=0.8
m+2
am+1=0.65,q=0.8
un
Fig. 1(a) and 1(b) show the correlations between replacement coefficient and the market share as well as profit of CSP 1 2 n−m 1 when u2c + · · · + um = 1.6 c = 1.8, un + un + · · · + un and q = 0.7. It can be seen that for a fixed value of the service rate, both fc1 and πc1 decrease as b increases. Fig. 1(c) shows the correlation between the connection rate and the profit when b11 = · · · = b1(n−m) = 0.5 and 1 2 n−m u2c + · · · + um = 1.6. Clearly, c = 1.8, un + un + · · · + un it shows that for a fixed value of the service rate, the profit of CSP 1 decreases when its connection rate increases. This can be understood by the fact that a higher connection rate means that the cloud service provider needs to invest more to improve its customer service quality which would inevitably increase its operational costs and decrease its profits. Fig. 1(d) and 1(e) depict the correlation between the service rate of NSP 1 and the market share as well as the profit of CSP 1 when q = 0.7, b11 = · · · = b1(n−m) = 0.5, u2c + · · · + um c = 1.8. We can see clearly from these two figures that a larger NSP service rate would yield a smaller CSP profit or market share.
u2n
Fig. 4.
=0.7,q=0.8
m+1
m+1
0.5 0.2
11
=0.55, b*
a
0.6
0.3
0.2
1
=0.55,q=0.65
a1=0.45,b11=0.7,q=0.7
0.7
11
a =0.65, b =0.65,q=0.8
0.7
11
m+1
m+1
a =0.75, b11=0.7,q=0.8
0.4
1
am+1=0.55, bm+1=0.65,q=0.8
a =0.45, b =0.7,q=0.65
11
a =0.65, b =0.6,q=0.8
* =0.55,q=0.6 m+1
=0.65, b
1
1
a
m+1
a =0.65, b =0.7,q=0.8
0.5
0.8
a1=0.45, b11=0.7,q=0.6,
un
1
am+1=0.75, bm+1=0.55,q=0.8
=0.8,q=0.7
m+2
0.9
0.45
0.8
0.4 0.3
0.4
0.5
0.6
0.6
0.8
u1n
1
1.2
u1n
(a)
(b)
Fig. 5. Correlation between the service coefficient a, q and Nash equilibrium.
we focus on the impacts of the internal elements of players (in this case, the service coefficient and the connection rate of service providers) on the values of the Nash Equilibrium. Throughout the experiments, we set Pkc = 1, k1c = 0.5, k2c = 1, Pkn = 0.8, k1n = 0.4, k2n = 0.8. 1) CSPs vs. CSPs: We choose CSP 1 and CSP 2 to typify the investigation into the competition between cloud service providers. By the study in Section III, we know that the profits of CSP 1 and CSP 2 are 1 1 2 πc (uc , uc ) = fc1 · Ukc (u1c ) , (15) πc2 (u1c , u2c ) = fc2 · Ukc (u2c ) and the service rates are ⎧ ⎨ u1 = c ⎩ u2c =
Pkc −k2c q 2k1c Pkc −k2c q 2k1c
+ +
u2c 2a1 u1c 2a2
.
(16)
B. Nash Equilibrium of service providers
The variations of a and q are shown in Fig. 3(a) and 3(b). The intersection point of the two straight (color-wised) lines in these two figures denote the service rates of CSP 1 and CSP 2 when a Nash Equilibrium is reached, and we use 2∗ (u1∗ c , uc ) to represent this equilibrium point. Fig. 3(a) shows the correlation between the service rate and the equilibrium 2∗ point. Clearly, we can see that (u1∗ c , uc ) goes down as the values of a1 and a2 go up. Fig. 3(b), in a similar fashion, shows the correlation between connection rate and the equilibrium point, and indicates that a higher connection rate would yield a smaller equilibrium service rates for CSP 1 and CSP 2.
We now turn our attention to the study of the Nash Equilibrium in the competition of the service providers. Nash Equilibrium is a critical notion in Game Theory which represents the “best point” in the interests of all game players. Here,
2) CSPs vs. NSPs: We now study the Nash Equilibrium resulted in from the competition between CSPs and NSPs. We choose CSP 1 and NSP 1 to typify our investigation. Similarly, by using the results in Section III, we have the following
formula
πc1 (u1c , u1n ) = fc1 · Ukc (u1c ) , πn1 (u1c , u1n ) = fn1 · Ukn (u1n )
and the service rates are ⎧ c c ⎨ u1 = Pk −kc 2 q + c 2k ⎩ u1 = n
b11 u1n 2a1 1 b∗ Pkn −k2n q (m+1)1 uc + 2k1n 2am+1
.
1
3) NSPs vs. NSPs: Finally, we look into the matter of the Nash Equilibrium effected in the competition between NSPs by typifying NSP 1 and NSP 2. Again, by the study in Section III, we have we have following formula 1 1 2 πn (un , un ) = fn1 · Ukn (u1n ) , (19) πn2 (u1n , u2n ) = fn2 · Ukn (u2n ) Pkn −k2n q 2k1n Pkn −k2n q 2k1n
+ +
u2n 2am+1 u1n 2am+2
.
(20)
Fig. 5(a) and 5(b) show the graphs of the equations in (17) with different values of the service coefficient and
2∗ connection rate. Evidently, the equilibrium point u1∗ n , un decrease as the service coefficient a increases, and decreases as the connection rate q increases as well. V.
C ONCLUSION
We have in this paper leveraged the Game Theory to model the competition on the cloud service market between the cloud service providers and the network service providers. Issues such as the Nash Equilibrium, correlations of replacement coefficients and connection rates with respect to market shares and profits of service providers, and the impact of replacement coefficients, service coefficients, as well as connection rates on the equilibrium point, are thoroughly investigated. Our main findings are as follows. •
•
A high connection rate means that a service provide would need to spend more on improving its customer service quality and therefore would result in more costs and less profits. As such, service provider may increase its profit by somehow lowering its connection rate.
•
A larger service coefficient indicates that a service provider’s market share and profit depend more on its service rate, and the service provider is more vulnerable to the fluid competition on the market.
•
The equilibrium point would increase when the service coefficient decreases, or the connection rate decreases, or the replacement coefficient increases.
(18)
The graphs of the equations in (16) with various values of service coefficient, connection rate and replacement coefficient are shown in Fig. 4(a), 4(b), and 4(c). Analogous to the case of CSPs vs. CSPs, we see that when other parameters 1∗ are fixed, the equilibrium point (u1∗ c , un ) decreases as the service coefficient a increases, decreases as the connection rate q increases, and increases as the replacement coefficient increases.
and the service rates are ⎧ ⎨ u1 = n ⎩ u2n =
make their business unique and multifarious to reduce the chance of being replaced by other peers.
(17)
A service provider with a small replacement coefficient has a competitive edge and a relatively high profit. Thus, service providers should consider how to
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