Concurrent and cooperative negotiation of resources in cloud computing: A game theory based approach

3.1 Agencies

The agencies of resource consumer, resource broker and resource provider have one or more static agents and database which are shown in Fig. 2. Table 2 lists set of notations used in description of the agencies framework.

3.2 Cooperative resource cost negotiation game

We proceed to model the RCAg-RBAg resource cost negotiation as a cooperative game, based on the following assumptions.

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Assumption 1: To motivate cooperative negotiation among CAs/BAs, payoffs are offered. Payoffs are monetary benefits offered to both party as an outcome of cooperative negotiation depending on the discount factor. The discount factor is taken into account while employing the player’s strategies in the game. This helps in achieving negotiable cost at faster rate. In other words, higher the discount factor in cooperative negotiation, more is the payoff earned, and lesser is the cost paid for acquiring the resource. In other words, the cost that needs to be charged by BA is inversely proportional to payoffs earned by the consumer. The players in the resource cost negotiation game are heterogeneous players, aiming at different payoffs.

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Assumption 2: We assume a game in which players know about the available actions and corresponding payoffs of other players but not their moves.

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Assumption 3: At any time the sum of the payoffs of both the players is a constant value, not equal to zero, i.e., a general sum game model; neither player wins in a zero-sum game.

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Assumption 4: Both the RCAg and RBAg have non-negative payoff functions (same reasoning as Assumption 3).

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Assumption 5: The criteria used to influence a broker agent’s decision are: (i) the utilization level of its resources, and (ii) recent requests from consumers for resources. If more resources are currently being used to execute tasks or are already leased to other consumers, then the broker is less likely to relax its negotiation terms. If there are fewer recent demands from consumers to lease its resources, a broker is more likely to slightly relax its negotiation criteria, since it is under more pressure to trade its idle resources. By slightly relaxing negotiation terms under intense negotiation pressure, both consumer and broker agents generally achieve higher success rates in negotiation (without sacrificing much of their average payoffs).

The consumer’s budget to amass resources is limited. Also, the resources vital for an application to run are limited in the data center of an ICSP acquired by RBAg. Hence cooperative resource cost negotiation between RCAg and RBAg is needed for achieving better payoffs. The RBAg offers services and receives compensation from the CA. The cooperative negotiation game considered consists of three factors: (i) set of players, i.e., CNA from RCAg and BNA from RBAg, (ii) strategies for each player, and (iii) payoff for each player.

Let CNA’s offer price for cooperating and deceiving be denoted by 𝑂𝑃 𝐶𝑁𝐴 and n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 , respectively, where . Also, let the BNA’s offer price for cooperating and deceiving be denoted by 𝑂𝑃 𝐵𝑁𝐴 and n ⁢ c ⁢ 𝑂𝑃 𝐵𝑁𝐴 , respectively, where . If RBAg decides not to allow expected quality of services (refer to expected quality of service as Q ), it saves cost but it risks the violation of SLAs which may result in even greater costs in terms of penalty. This encourages RBAg to play a cooperative resource cost game.

The RCAg’s experience, on services received from RBAg, could be quantified in terms of satisfaction, where a service delivered on expected lines, i.e., of quality Q , results in satisfaction s ⁢ ( Q ) . On the other hand, if the service delivered is not on the expected lines, i.e., of quality Q ′ , the satisfaction is s ⁢ ( Q ′ ) , where .

The interactions between CNA and BNA could be recursive in resource cost negotiations. In such relationships, the players do not seek the immediate maximization of payoffs but instead the long-run optimal solution. Such situations are modeled in game theory by repeated game models. We consider the RCAg-RBAg interaction model as an infinite horizon repeated game, since the RCAg may keep requesting RBAg for the particular service, but the number of such requests are not known well in advance.

A repeated game makes it possible for the players to condition their negotiation moves on the complete previous history of the various stages, by employing strategies that define appropriate actions for each iterations. In our scheme, the harsh trigger strategy is used by the CNA, such that if the CNA is not satisfied in one of the stages, the CNA may punish BNA by leaving the relationship forever in the next stage, e.g., stop interacting with the specific RBAg for subsequent requests of the particular service. Given such a strategy, the BNA has stronger incentives to cooperate and provide the service promised, since it faces the threat of losing its consumers from RCAg. Another popular strategy used in this scheme is for a player to mimic the actions of his opponent, giving him the incentive to play cooperatively. This way the player will be rewarded with a similar replicating behaviour. We refer to this as a tit-for-tat strategy.

We employ the harsh strategy as a viable strategy for the CNA and the tit-for-tat strategy as a feasible strategy for the BNA. In addition, we define two more probable strategies for the CNA, and one more desirable strategy for the BNA. For the CNA we define: (a) the deceive-and-exit strategy, and (b) the deceive-and-joinback strategy. For the BNA, we define the deceive-and-join-back strategy. The deceive-and-exit strategy is defined so as to allow the CNA to employ non-cooperative behaviour. With this strategy, the CNA leaves after deceiving from cooperation, i.e., does not continue interaction with the particular BNA, in order to avoid any punishment for deceiving. The deceive-and-join-back strategy is defined to capture a case where the BNA deceives and joins back in the subsequent iterations. It is a cooperative strategy that provides the opportunity for the BNA to join back and cooperate with CNA, without penalising it heavily. The discount factor is taken into account while employing the strategies.

In order to compare different sequence of payoffs in repeated games, we utilize the idea of the present value of a payoff sequence, and refer to it as the current payoff value (CPV). CPV is the sum that a player is willing to accept currently instead of waiting for the future payoff, i.e., accept a smaller payoff currently that will be worth more in the future; similar to making an investment in the current iteration that will be increased by a rate r in the next iteration. Hence, if the payoff in the next iteration were equal to 1 (normalized maximum value), currently the payoff a player willing to accept is 1 1 + r . If there is a probability that the game will not continue in the next iteration, equal to p , then the payoff a player willing to accept currently is 1 - p 1 + r . Thus, d ⁢ f = 1 - p 1 + r , where d ⁢ f ∈ [ 0 , 1 ) refers to the discount factor in repeated games.

3.3 Payoffs calculation

For an infinitely repeated game, CPV includes the discounted payoff of all subsequent iterations of the game. Let the payoff from the current iteration be equal to 1. Then, the additional payoff a player willing to accept in an iteration equals to ( d ⁢ f ) r where r is the iteration number. Thus 𝐶𝑃𝑉 = 1 1 - d ⁢ f (by applying summation of geometic series formulae). For a payoff P payable at the end of each iteration, the CPV equals P 1 - d ⁢ f . In order to determine better strategy for several iterations of game, we utilize the idea of CPV and observe for which values of d ⁢ f = 1 - p 1 + r , a given strategy of a player is best response to the other player’s strategy.

Next we present several strategies for payoff calculations.

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CNA playing the harsh strategy. BNA could either play the tit-for-tat strategy, i.e., cooperate in the current iteration, or play the deceive-and-join-back strategy. If the BNA cooperates, then: 𝐶𝑃𝑉 c 𝐵𝑁𝐴 = | 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 | 1 - d ⁢ f . If the BNA deceives, then: 𝐶𝑃𝑉 n ⁢ c 𝐵𝑁𝐴 = 𝑂𝑃 𝐶𝑁𝐴 - n ⁢ c ⁢ 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f .

CPV for BNA in case of cooperation must be greater than CPV in case of non-cooperation. Thus, ${\text{𝐶𝑃𝑉}}_c^{\text{𝐵𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐶𝑁𝐴}}=\frac{{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}{1-df}>{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}+\frac{df.0}{1-df}$ . If the CNA plays harsh strategy, BNA cooperates when $df>\frac{{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}{{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}$ .

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CNA playing the deceive-and-exit strategy. Considering BNAs possible strategies, it could either cooperate or deceive in the current iteration. If BNA cooperates then: 𝐶𝑃𝑉 c 𝐵𝑁𝐴 = n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If BNA deceives then: 𝐶𝑃𝑉 n ⁢ c 𝐵𝑁𝐴 = n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 - n ⁢ c ⁢ 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If CNA plays deceive-and-exit strategy, BNA is not motivated to cooperate since ${\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐵𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_c^{\text{𝐵𝑁𝐴}}$ .

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CNA playing the deceive-and-joinback strategy. Considering BNAs possible strategies, it could either cooperate or deceive in the current iteration. If BNA cooperates then: 𝐶𝑃𝑉 c 𝐵𝑁𝐴 = s ⁢ ( Q ′ ) - 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If CNA deceives then: 𝐶𝑃𝑉 n ⁢ c 𝐵𝑁𝐴 = s ⁢ ( Q ′ ) - n ⁢ c ⁢ 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If CNA plays deceive-and-joinback strategy, BNA may not cooperate, since ${\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐵𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_c^{\text{𝐵𝑁𝐴}}$ .

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BNA playing tit-for-tat strategy. If CNA cooperates then: 𝐶𝑃𝑉 c 𝐶𝑁𝐴 = | 𝑂𝑃 𝐵𝑁𝐴 - 𝑂𝑃 𝐶𝑁𝐴 | 1 - d ⁢ f . If the CNA deceives then: 𝐶𝑃𝑉 n ⁢ c 𝐶𝑁𝐴 = 𝑂𝑃 𝐵𝑁𝐴 - n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . For the CNA to be motivated for cooperation, CPV in case of cooperation must be preferrable than CPV in case of non-cooperation. Thus, ${\text{𝐶𝑃𝑉}}_c^{\text{𝐶𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐶𝑁𝐴}}=\frac{{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}-{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}}{1-df}>{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}+\frac{df.0}{1-df}$ . If the BNA cooperates, the CNA is motivated to cooperate when: $df>\frac{{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}}{{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}$ .

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BNA playing the deceive-and-joinback strategy. Considering CNAs possible strategies, it could either cooperate or deceive in the current iteration. If CNA cooperates then: 𝐶𝑃𝑉 c 𝐶𝑁𝐴 = s ⁢ ( Q ′ ) - 𝑂𝑃 𝐶𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If CNA deceives then: 𝐶𝑃𝑉 n ⁢ c 𝐶𝑁𝐴 = s ⁢ ( Q ′ ) - n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 + d ⁢ f ⁢ .0 1 - d ⁢ f . If BNA plays deceive-and-joinback strategy, CNA is not motivated to cooperate since ${\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐶𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_c^{\text{𝐶𝑁𝐴}}$ .

3.4 Punishment strategy

Given a history of the game where both players have cooperated in the past, we seek the values of d ⁢ f that can motivate cooperation under one-iteration punishment strategy. If CNA has decided to cooperate for the current iteration, the BNA has two options: to cooperate or to deceive. If the BNA cooperates, the CPV will consist of the payoff in the current iteration, plus a discounted version of this payoff for all the rest of the iterations, represented by Eq. (7). Terms 1 and 2 correspond to cooperation and deceiving, respectively. We consider the first two iterations separately in order to compare the current value when deceiving, since the behaviour of the BNA alternates in such iterations of the game. Term 3 corresponds to the CPV when the player joins back in the negotiation process.

𝐶𝑃𝑉 c 𝐵𝑁𝐴 = ( 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 ) + d ⁢ f . ( 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 ) ⁢ + ( d ⁢ f ) 2 . ( 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 ) 1 - d ⁢ f(7)

If the BNA deceives, the CPV is sum of BNA’s payoff in the current iteration and the successive iterations and payoff in the rest of the game iterations. This is represented by Eq. (8).

𝐶𝑃𝑉 n ⁢ c 𝐵𝑁𝐴 = 𝑂𝑃 𝐶𝑁𝐴 - n ⁢ c ⁢ 𝑂𝑃 𝐵𝑁𝐴 + d ⁢ f ⁢ .0 ⁢ + ( d ⁢ f ) 2 . ( 𝑂𝑃 𝐶𝑁𝐴 - 𝑂𝑃 𝐵𝑁𝐴 ) 1 - d ⁢ f(8)

In order for cooperation to be motivated, it must satisfy the condition, ${\text{𝐶𝑃𝑉}}_c^{\text{𝐶𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐵𝑁𝐴}}$ . The condition can be simplified to $df>\frac{{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}{{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-{\text{𝑂𝑃}}_{\text{𝐵𝑁𝐴}}}$ . If the BNA decides to cooperate in the current iteration, the CNA has two options: cooperate or deceive. The CPV of the CNA, while cooperating, is the sum of current payoff and the discounted payoff for the next iterations, and the discounted payoff for the rest of the infinitely repeated game, which is represented by Eq. (9). We consider three discounted iterations to facilitate the comparison with the CNA’s CPV in case it deceives.

𝐶𝑃𝑉 c 𝐶𝑁𝐴 = s ⁢ ( Q ) - 𝑂𝑃 𝐶𝑁𝐴 + d ⁢ f . ( s ⁢ ( Q ) - 𝑂𝑃 𝐶𝑁𝐴 ) ⁢ + ( d ⁢ f ) 2 . ( s ⁢ ( Q ) - 𝑂𝑃 𝐶𝑁𝐴 ) 1 - d ⁢ f(9)

If the CNA deceives, the CPV is a sum of current payoff, the discounted payoff in the next iteration, and the cooperation payoff discounted for the rest of the game, represented by Eq. (10).

𝐶𝑃𝑉 n ⁢ c 𝐶𝑁𝐴 = s ⁢ ( Q ) - n ⁢ c ⁢ 𝑂𝑃 𝐶𝑁𝐴 + d ⁢ f . ( s ⁢ ( Q ′ ) - 𝑂𝑃 𝐶𝑁𝐴 ) ⁢ + ( d ⁢ f ) 2 . ( s ⁢ ( Q ) - 𝑂𝑃 𝐶𝑁𝐴 ) 1 - d ⁢ f(10)

In order for cooperation to be motivated, ${\text{𝐶𝑃𝑉}}_c^{\text{𝐶𝑁𝐴}}>{\text{𝐶𝑃𝑉}}_{nc}^{\text{𝐶𝑁𝐴}}$ , which on simplification gives $df>\frac{{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}-nc{\text{𝑂𝑃}}_{\text{𝐶𝑁𝐴}}}{s(Q)-s(Q^{\prime })}$ .

The cooperation limits for each player (BNA and CNA), with several strategies used by an opponent, are summarized in Table 5.

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The interaction of agents in game is shown in Fig. 3, where nodes represent agents, solid lines represent communication messages. Agents in RCAg, RBAg, and RPAg cooperatively work together to discover suitable VMs with optimal cost for service execution of jobs. The sequence of operations in the proposed scheme are as follows:

12. 1.

Consumer agent sends job execution request to Broker agent.

2.

Broker agent communicates to Job allocation agent about resource requirements.

3.

Job allocation agent informs Match maker agent to recommend specified number of suitable VMs, which fulfills the resource requirements.

4.

Match maker agent searches logs and discovers suitable VMs that meet job requirements (logs hold resource history containing details of each used VMs).

5.

Match maker agent sorts VMs in descending order of required resource.

6.

Match maker agent recommends expected number of VMs to Job allocation agent.

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Job allocation agent informs Broker agent to decide optimal cost of VMs.

8.

Broker agent triggers Broker negotiation agent to play a cooperative negotiation game with Consumer negotiation agent to negotiate resource cost.

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Consumer negotiation agent and Broker negotiation agent play cooperative resource cost negotiation game.

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Broker negotiation agent returns the cost of each VM (satisfiable to both negotiating agents) to Job allocation agent.

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Job allocation agent schedules jobs to Resource provider agency, and receives result from them after execution.

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Job allocation agent sends job results to Consumer agent.

In the steps 8 and 9, the cooperative negotiation strategies like Harsh-trigger, Deceive-and-exit, Deceive-and-Joinback, or Tit-for-tat are used (discussed in Sections 3.2 and 3.3). Strategies may be selected based on payoffs required by the negotiating agents.

3.6 Example

A simple example is provided demonstrate the proposed scheme. Consider a single node each for RCAg (namely A), RBAg (namely B), RPAg (namely C), and ICSP (namely D). The resource availability at D is indicated as (x, y, z, t), where x, y, z and t denotes the VMs size, its quantity, cost of VM, and the time duration of its availability, respectively. Let the availability at D be (small, 1, $1.10, 60 sec.). Let us assume that several job requests arrive at node A, with each job requires a 60 sec. execution time. When this requirement is communicated to B, it computes the cost of fulfilling the resource requirements as (small, 20, $22, 60). But, A refuses to pay $22 for each job. This scenario encourages B to negotiate the resource cost. Following is the sequence of operations that takes place during the cooperative negotiation game.

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A starts the resource negotiation game by stating the price, p, that it can pay ( = $18) per job.

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B queries C regarding the updation of (x, y, z, t) for serving multiple consumer. Let the returned value be (small, 50, $50, 60).

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B queries A regarding the expected start time (est) of the job, and the number of jobs to be submitted (NJ). A responds as, est = ‘x’ time, and NJ = 20.

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B initially negotiates with increasing price, i.e. p $>$ $18, est = ‘y’ time, and VMs quantity, y = 15.

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In the subsequent negotiations, B provides competitive offers to A, with lesser p and offers to supply more NJ. B warns A, to increase p, if NJ is decreased (as it may underutilize its resource).

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Following are the game strategies that A and B can make use of to achieve optimal values of their negotiations. The optimal value is such that it does not cause any loss to either A or B.

1. (a)

A decides to employ Harsh strategy for negotiation, and agree to B’s demand (i.e. p $>$ $18). Outcome: B may not be satisfied if A is dissatisfied with its QoS, leading to non-cooperation in future by A. It may not lead to optimal solution, for most of the negotiations.

(b)

A or B decide to employ Tit-for-Tat strategy. In other words, A pays p = $18.5, and B promises est = ‘z’ time (which is near to ‘x’ time) and VMs quantity, y = 18 (which is sufficient to serve 20 jobs, if some of the applications are parallelized). Outcome: Both A and B shall replicate each other’s behavior, paving for cooperation in future. It may lead to optimal solution, in most of the cases.

(c)

A decides to deceive B (e.g., by not paying the promised cost), and exit after receiving services. Outcome: B may not accept to provide services to A in future, or it may do so after penalising it heavily, leading to non-cooperation for most of the time. It is not a optimal solution, for most of the negotiations.

(d)

A decides to deceive B (e.g., by not paying the promised cost), exit, and join-back for the services from B. Outcome: B may accept to provide services to A in future, provided A clears all the penalty imposed during the previous negotiations, leading to cooperation for most of the time. It may result in an optimal solution, for most of the negotiations.

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A and B finally agree to Tit-for-Tat strategy, and lock the negotiation at (small, 18, $18.5, 60), with est = ‘z’ for job execution. This ensures better service request/response by A and B, respectively. It leads to cooperative negotiations, gives optimal negotiated price, and increase the payoffs of both the entities for future services too.

Without the agent approach, the flexibilty for cooperative and concurrent facilitation of negotiation activities between many-to-many consumer, broker, and different groups of provider agents shall not be possible, leading to non-optimal solutions.

3.6.1 Complexity of the communication between CA, BA, and PA

The communication complexity is determined by the number of messages exchanged between agents. When a CA submits its requirement to a BA, it sends proposal messages to n BAs. After receiving the proposals, the CA sends an accept-proposal message to only one BA, after x rounds of negotiation. Then, the BA sends m proposals to the PAs for checking availability of resource(s). Thus, the complexity for the model behavior is bounded by O ⁢ ( n ⁢ x ⁢ m ) .

4.1 Simulation model

The simulated cloud environment consists of RCAg, RBAg, RPAg and ICSPs. The behavior of ICSPs considered is similar to that of Amazon EC2, and Microsoft Azure, discussed in http://www.tomsitpro.com [42]. The values of simulation parameters are presented in Table 6. The implementation of the CNA-BNA interactive negotiation game is based on a publicly available Matlab implementation of the Iterated Prisoner’s Dilemma Game, given by Taylor [46], which has been extended to include all existing and proposed strategies examined in Section 3. We use simple numbers as payoffs to get scores for different strategy combinations. These numbers follow the relationships of the payoffs, as described in general case in the repeated game models. The payoffs for the different simulation sets are summarized in Table 7.

4.2 Performance parameters

For comparison with existing works, we have considered waiting time, negotiation time, execution time, successful job offers, resource utilization rate and resource pricing, as these are important parameters in testing the efficiency of the proposed scheme. Additionally, payoffs are analyzed to check the effectiveness of the scheme, but owing to lack of rigorous available works, it is not compared with existing schemes.

The performance parameters are defined as follows.

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Waiting, negotiation and execution time: Waiting time is the time taken to analyze the job/resource request, and searching the possible RBAg(s) which could fulfill the request of the RCAg(s). Negotiation time is the time taken by BNA and CNA to negotiate resource cost using cooperative game. Execution time is the time taken to process the consumers job requirements.

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Successful job offers: It is ratio of the total number of jobs executed to the total number of jobs submitted to the RBAg in any given time interval.

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Resource utilization rate: It is ratio of the job processing rate to job arrival rate.

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Payoffs: Payoffs indicate the profit of BNA and CNA obtained during the cooperative negotiation game.

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Resource pricing: It is the value of resource that reflects its economic value.

4.3 Simulation procedure

The simulation procedure is as follows.

1. 1.

Deploy RCAg, RBAg and RPAg in the cloud environment;

2.

Submit concurrent jobs from RCAg to RBAg for resource analysis;

3.

Employ MMA to find the eligible VMs and then recommend required number of VMs;

4.

Employ BNA to play concurrent negotiation game with CNAs for negotiating resource cost;

5.

Employ JAA to schedule user jobs to RPAg, collect results from RPAg and sendback to CAs;

6.

Compute the performance parameters.

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Table 6

Simulation parameters

Symbol	Values
RCAg	[50–100] nodes
RBAg	[250–500] nodes
RPAg	[250–750] nodes
ICSP	4 nodes
Mappers	[5–10] nodes
Reducers	[3–5] nodes
Quantity of resources per BA	[10–50] VMs
Unit cost of a resource	[10–100]$
No. of resource types per CA	[1–10] VMs
VMs per ICSPs	[25–400] nodes
Processor’s speed	[2, 4] Mghz
Processor’s memory	[4, 8] GB
Jobs	[50, 500] applications
Jobs arrival rate	[5–100] jobs/ms.
Payoffs	[0–90]$
Jdeadline	[60, 600] sec./job
Max_negotiations	[2–10] iterations
Consumers	[10–250]
Buffered resource	[100–200] VMs

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Table 7

Payoffs for different simulation sets

Strategies	Simulation set 1	Simulation set 2	Simulation set 3
User leaves	(0, 0)	(0, 0)	(0, 0)
One defects, one cooperates	(4, 1)	(100, 1)	(90, 10)
Both defect	(2, 2)	(40, 40)	(50, 50)
Both cooperate	(3, 3)	(60, 60)	(60, 60)

4.4 Results

This section presents the results of the proposed scheme and the existing works, by using simulation. The following notations have been used in the discussion of results of the proposed and existing works. The proposed work is denoted as GTBNSMM (Game theory based negotiation in Many-to-Many). The existing works are denoted as GTBBOO (Game theory based bargaining in One-to-One) [43], CFSC (Coalition formation for Service Composition) [44], CMOS (Cooperation multi-organization scheduling) [45], GTBRA (Game theory based resource allocation) [35], ORAP (Online resource allocation and pricing) [37], ABC (Agent based cloud) [38].

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