Saturday, March 30, 2019
Two different queuing systems
2 unlike queuing remainssIntroductionThis report presents the modeling of twain different queuing establishments in a typical lingo environment victimization the field of battle softw ar. The boldness musical breakups for both the transcriptions atomic number 18 constructed based on the simulation results. The agreements be therefore compared to find out which queuing system performs better.AssumptionsFor both systems, no real selective information was collected. Both the interarrival times and service times were taken from known luck distributions. Other assumptions to a fault include no balking, reneging and adjust jumping. Each restitution had the same initial conditions and terminating events. Lastly, both systems are assumed to be s put off, take over infinite calling population and no limit on system capacity.Modeling of the systemsIn this section of the report, the actual modelings of both the systems victimisation the arena software are discussed. Configurat ion of the models and steps to run the system are similarly highlighted. Firstly, system 1 is explained, followed by system 2.System 1 modelingSystem 1 has a separate queue for distributively individual bank teller. found on Kendalls notation, system 1 is an M/M/4 system. It is a Poisson process and disallows batch arrivals. The table downstairs summarizes the categorization of the system based on the contentions of the system.In this system, nodes arrive and carry to join the shortest queue. The highlighted mean values in the table represent the exponential mean value ?. For the interarrival time, 100 guests arrive in 1 hour. Hence,= 1/ (100/60) = 0.6Firstly, manufacture the customer arrival portion by clicking and dropping the create button. Next con bit it by doubling clicking the diagram. The Figure shows the dialog cut to configure the entity.Type the parameter as shown in Figure 2 above for this system. The configuration can also be shown in the figure below.Create the four individual processes for severally of the Bank Tellers by using the process button. Configure the process as shown below.Since the customers can choose the shortest queue to join upon arrival, create a decision box by using the decide button. Configure the decision box as follows prate on the Add button to include the conditions for the branching conditions. Select Expression and discipline click and select expression builder to construct the expressions.Finally, create the customer departure by using the Dispose button. Double click on the button to configure by naming it.Lastly, connect all the components in concert to model the system 1.System 2 modelingSystem 2 has only a single queue for all the arriving customers. When a bank teller becomes available, the customer will be served by that bank teller. Based on Kendalls notation, system 2 is an M/M/1 system. The table below shows the categorization of the system 2 based on Kendalls notation. discharge the assumptionOn ce the models of both the system are constructed, simulation runs are conducted to evaluate the performance of the systems. The steps in running the simulation are as follows put over on the Run tab and select Setup.Click on the Replication Parameters tab. Input number of counters as 15 and replication length as 480 change all the units to minutes. This is shown in the Figure below.Click on Run tab and select Go to run the simulation.Simulation ResultsThis section of the report summarizes the results produced by both the queuing systems. The performance measure parameter is the modal(a) time the customer spends in the bank. The results for each individual system are evaluated and the following confidence interval is constructed. Then the two systems are compared by constructing an different confidence interval.System 1 ResultsThe system 1 results are based on the average time a customer spends in the system as its performance measure. The average time for each replication is summa rized in the table below.Firstly, the mean is computed using(n) = 4.8121Variance is also computed using(n) = 1.103800987Hence the 95% confidence interval (? = 0.05, t14, 0.975 = 2.145) for system1 is computed using arrogance interval 4.2302, 5.3940System 2 ResultsThe system 2 results are also measuring the average time the customer spends in the system. The results are summarized in the table below.By using the same formulas, the mean, variance and confidence interval are as follows(n) = 3.804533333(n) = 2.231921051Confidence interval 2.9771, 4.6319Comparison between deuce SystemsFrom previous results, the confidence intervals of both the systems overlap each other. Therefore, it is hard to define which system performs better. Hence, paired- t confidence interval is used to compare the two systems. It is important to note that the number of replications for each system must be the same for this type of comparison. The table below summarizes the results of this comparison.The mean, variance and the confidence interval is computed and the results are as follows(n) = 1.007566667(n) = 3.578001252Confidence interval 0.5192, 1.4960Since the confidence interval does not contain zero, there is strong evidence to conclude that system 1s average time customer spends in the system is larger than that of system 2. Hence, system 2 performs better than system 1.ConclusionThis report presents the models of two different queuing systems in a bank environment. Through the simulation results, it is found that system 2 performs better than system 1. In order to get much accurate results, the number of simulation runs must be increased and other performance measure parameters can be tested to further sess the performance of both the systems.