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# (Solved): Wait Line Configuration [100 marks] As part of designing a clinic's wait line, we have the option to ...

Wait Line Configuration [100 marks] As part of designing a clinic's wait line, we have the option to set up either multiple singleserver queues (similar to those found in grocery stores) or a single multiple-server queue (similar to those found in banks) with both configurations having the same total arrival and service rates. "Multiple Single-Server Queues" "A Multiple-Server Queue" For our clinic, we are considering two types of queue configurations as follows: A. Grocery store queue model: Design three single-server queues, where each server has arrival rate

(\lambda )

of 5 , service rate

(\mu )

of 6 , and number of servers (s) of 1 . B. Bank queue model: Design a single three-server queue, where arrival rate

(\lambda )

is 15 , service rate

(\mu )

is 6 , and number of servers (s) is 3 . Task 1: Use the Q.xis template to fill the table below [50 MARKS]: \table[[\table[[Performance],[Measure]],\table[[Three M/M/1],[Single-Server Queues],[(Grocery Store)]],\table[[One M/M/3],[Three-Server Queue (Bank)]]],[Utilization,,],[

L_(q)

,,],[

W_(q)

,,],[W,,]] Hint: for

L_(q)

and

L

of three

(M)/(M)/1

queue configuration, you need to multiply the result in

Q.x|s

|| by 3 because there are three independent servers in total. Task 2: Discuss which queue configuration you prefer and why [50 MARKS]. 2

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