Question: With exponentially distributed arrival and processing times consider two queue configurations: 1) a single queue with two servers operating at the same rate and 2)

With exponentially distributed arrival and

With exponentially distributed arrival and processing times consider two queue configurations: 1) a single queue with two servers operating at the same rate and 2) two queues each served by a single server and both servers operate at the same rate. To be clear - all servers operate at the same rate and customers arrive at the same rate in both configurations - the only difference is the queue configuration. Which of the following is most likely to be true? Note: Configuration 1 - M/M/2 Queue with arrival rate and each of the 2 servers process customers at a rate Configuration 2 - Each of the 2 queues are M/M/1. For each M/M.1 queue, arrival rate is 2/2; and server rate is Hint: While you can mathematically show the relationship, it would help (and would be much easier) to choose numbers for 2 and to aid in the comparison. While choosing numbers for arrival rate and service rate, please ensure that > 2/2 for the queue systems to be feasible. Hint: 2 Options: Option 1: Use MM1 and MM2 formulas to see which configuration has the smaller W. While you can mathematically show the relationship, it would help (and would be much easier) to choose numbers for and u to aid in the comparison. While choosing numbers for arrival rate and service rate, please ensure that > 2/2 for the queue systems to be feasible. Option 2: Conceptually, you can think about the different factors that impact waiting time and see which configuration would be least impacted. a) Average waiting time in configuration 1 is less than configuration 2 b) Average waiting time in configuration 1 is equal to configuration 2 c) Average waiting time in configuration 1 is greater than configuration 2

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