Modeling the Negotiation of Agents in MAS and Predicting the Performance – an SPE Approach

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Introduction
A Multi-Agent System (MAS) is usually understood as a system composed of interacting autonomous agents. MAS have been employed successfully in a number of scenarios. The important characteristics of the agents which distinguish it from an object are Autonomous, Cooperation, Goal oriented, Adaptability, Mobility, Negotiation etc. Many articles on MAS have been mainly concerned with functional characteristics such as coordination, rationality and knowledge modeling. The nonfunctional characteristics also have the equal importance as the functional characteristics for any software system [1][2][3][4][5].
This research aims at making a contribution towards the non-functional characteristics Performance of agents in a MAS by considering the negotiation character of agents. Software Performance Engineering (SPE) is a method for constructing software systems to meet the performance objectives at the early stages of Software Development Life Cycle (SDLC). In SPE, system does not exist so it is not possible to develop the work load parameters from measurement data. Therefore, models of the system are used to collect the data required to predict the performance. The different data required for the SPE approach are Workload scenarios, Performance goals, Software Design concepts, Execution environment and Resource usage estimates [5][6][7].
The performance prediction of agents by considering the cooperation character of agent the authors have published different articles in [8][9][10][11]. In the early development stages measuring the negotiation workload and predicting the performance remains an important but largely unsolved problem. The problem of uncertainty regarding the negotiation workload is required to be addressed by estimation techniques. Hence, in this chapter a model for the negotiation scenario among the agents in a given time horizon is developed. The fitness function which represents the fitness of the agent in the negotiation scenario among 'n' agents in MAS is considered while framing the model. The negotiation workload obtained from the probabilistic model is integrated with the representative workload of the agents for predicting the performance of agents in MAS [12][13][14].
The tool SMTQA is used for obtaining the performance metrics. The execution environment is analyzed by considering various configurations in the hardware resources based on the dynamic workload of the negotiation agents over a time horizon. From the sensitivity analysis, the bottleneck resources are identified and suggestions for improvement of the software are made [15].

Methodology
A methodology is proposed to model the negotiation scenario of agents in a MAS using probabilistic approach. This is based on the methodology discussed for the distributed systems in [15]. Let t [t0, T+ t0-1] be the interval, where T be the number of intervals, to be the initial interval of the given time horizon. Let ST be the negotiation services that are considered to be executed during the T intervals. With these assumptions, we have devised the methodology as follows, • Developing a mathematical model for demand of negotiation services over a given time Each negotiation service that can be occurred in the interval t [t0, T+ t0-1], is characterized by: • Pijk(t),eprobability of occurrence of the e th negotiation primitive of those specified at time interval t • ,expected demand for each negotiation services sST, if the e th primitive occurs among those specified at time interval t.
Based on such specification of expected primitives, st demand scenarios can be generated in each interval t, where pij,s(t) be the probability that s th scenario occurs at time t when agent 'i' negotiates with the agent 'j'.
In the first period t0: , the number of scenarios can be recursively computed as: Each workload scenario can be defined as the occurrence of one event at period t given one scenario in the previous period t-1. Definition of the demand scenarios based on the specification of six events over a time horizon constituted of three intervals is given in Table 1.

Period
Event Probability Demand

Calculation of workload
The model is simulated by considering three time intervals such that for a given time interval t, t[0, 2]. The state (negotiation scenario) of the application in time t depends on the state (negotiation service scenario) at the time interval t-1 and the type of the request arrived at t. Hence the scenarios of the negotiation service are considered as states of the software application and the pattern of execution of negotiation services are modeled using the UML, State Chart Diagram. The Figure 2 to Figure 4 represent the workload to be executed during the different time duration. The negotiation services which are having a very less workload are executed during time t=0. During the time t=1 the negotiation services having a higher workload are executed. At time t=2, the negotiation services having an average workload are executed. From Figure 5, it is observed that agent a1 and agent a3 are negotiating more with agent a4. Also agent a2, agent a4, agent a5 are negotiating more with agent a3.

Simulation results
The scenarios of the negotiation primitives are simulated using the tool SMTQA, and the performance metrics are obtained and tabulated in

Sensitivity analysis
Simulation of the behavior of the resources is carried out by considering the configurations C1 to C6 is as follows. C1:-Processing speed of CPU is 2000, and the Internet speed assumed is 96. C2:-Processing speed of CPU is 3000, and the Internet speed assumed is 96. C3:-Processing speed of CPU is 4000, and the Internet speed assumed is 96. C4:-Processing speed of CPU is 2000, and the Internet speed assumed is 146. C5:-Processing speed of CPU is 3000, and the Internet speed assumed is 146. C6:-Processing speed of CPU is 4000, and the Internet speed assumed is 146.
The results of the different simulation runs are presented in the form of tables. The results obtained for Agent 1 for the different configurations considered is presented in Table 3. The maximum time taken by the Agent 1 to respond is 0.036 in the configuration C4 and minimum time taken to respond is 0.003 with configuration C1. The waiting time in Agent1 is also maximum for the configuration C4. This is due to the configuration of C1; the number of negotiation services dropped is more due to the low configuration of the      The results obtained for Agent 2 for the configurations considered are tabulated in the Table 4. Agent 2 has taken the maximum time 0.607 to respond under Configuration C1 and the minimum time to respond is 0.009 with configuration C5. Figure 21 presents the average dropping of requests and probability of idle time of Agent 2. The maximum number of requests is dropped in configuration C1. The maximum waiting time for the requests is observed with configuration C1. This has happened because Agent2 has received more requests.  The results obtained for Agent 3 for the configurations considered are presented in Table 9.5. Agent 3 has taken the maximum time 0.118 to respond under Configuration C4 and the minimum time to respond is 0.003 with configuration C5. The average dropping of requests and probability of idle time of the Agent 3 is plotted in Figure  23. The maximum number of requests is dropped in configuration C4. The maximum waiting time for the requests is observed in configuration C4 for Agent 3.
The Table 6 presents the results obtained for Agent 4 for the different configurations considered Agent 4 has taken the maximum time 0.033 to respond under Configuration C3 and the minimum time to respond is 0.008 with configuration C1. The maximum number of requests is dropped in the configuration C3. The maximum waiting time for the requests is observed with configuration C3.  requests it received. Also we observed that when the Internet speed is increased the dropping of requests reduced which gives the inference that many negotiation requests are executed by the agents successfully.

Summary
In this work, we presented a methodology to model the negotiation between the agents and predicting the performance of the system. We presented methodology to: i) develop a mathematical model for the workload of negotiation scenarios over a time horizon, ii) modeling the execution environment, iii) and iv) analyzing the execution environment for variations in resource configurations. The sensitivity analysis is done by considering modification in the resource configuration one at a time, and it also describes bottleneck resources. The output showed that how the different configurations of resources affect the response time of the agents.