Option A: Two servers, one queue Option B: Two servers, two queues Customers arr

Question

Option A: Two servers, one queue Option B: Two servers, two queues Customers arrive with a Poisson distribution with a rate lambda = 1 very 5 minutes. The servers have a deterministic service time of 5 minutes per customer. What are the types of queues for the two possible queueing systems? Are the queues stable? What are the queueing delays for each scenario? Which scenario is better? What if the servers split jobs, with one taking the orders and payments and the other one giving the food? In this scenarios, customers will use a common queue for the first server, and then they will queue for next server. What type of queueing system is this? Is it stable?

Explanation / Answer

1) There are three types of Queues,

Transient State

Steady State

Explosive State

Out of three there are two possible queuing are Transient State, Steady State.

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2) First option queue is stable because waiting time and service time are independant. two serve and one queue

But second option is not stable, because waiting time and service time are dependant. two serve and two queue

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3) Queue Delay is not applicable for first option because customer is not waiting for the server

Queue Delay is applicable for second option because customer can wait due to two server and two queues.

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4)First option sceranio is better because the customer is not waiting

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