Question: A queueing system is being designed. The inter-arrival times of customers are expected to be exponentially distributed with mean 1/ = 50 seconds. Three different

A queueing system is being designed. The inter-arrival times of customers are expected to be exponentially distributed with mean 1/λ = 50 seconds.

Three different options are being considered:

• One single-server queue with infinite buffer space. The service times are exponentially distributed with mean 1/µ = 20 seconds. Model this scenario as an M/M/1 Queue and find the expected customer waiting time.

• Two single-server queues, each with infinite buffer space. Customers are randomly dispatched to each queue with an equal probability. The service times are exponentially distributed with mean

1/µ = 40 seconds at each server. Model this scenario as a pair of M/M/1 Queues, being sure to adjust the λ-value to reflect the additional queue. Find the expected customer waiting time.

• One two-server queue with infinite buffer space. The service times are exponentially distributed with mean 1/µ = 40 seconds at each server. Find the response time in each option using queueing analysis. Model this scenario as an M/M/s Queue where s is 2. Use the Erlang C Formula to determine the expected customer waiting time.

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