Question

QUESTION 2:

Consider a check–out station at a small store with customer arrivals described by a Poisson process with intensity ? = 10 customers per hour. There are two service team members, Tom and Jerry, working one per shift. In Tom’s shift, the service times are exponentially distributed with the mean time equal to 3 minutes, while for Jerry service times are exponentially distributed with the mean time equal to 5 minutes.

1. Find the mean queue length during the shift served by Tom. 2. Find the mean queue length during the shift served by Jerry.

I need help on question 3 please,question 2 is given as a refrence.

Problem 3: 10 points Continue with Tom and Jerry from the previous problem. Customers arrive for service with the rate ? = 10 per hour. When they are served by Tom, the service time is exponentially distributed with the mean equal to 3 minutes. However, service times by Jerry are exponentially distributed with the mean equal to 5 minutes As the holiday season was approaching, both Tom and Jerry worked simultaneously, at two different counters, so the individual service me, Y became the minimum of two independent exponentially distributed variables Y = min [T, J]. where T is the service time for Tom and J is the service time for Jerry 1. Determine the birth-and-death parameters for this queueing system. 2. Derive the stationary distribution of the number of customers waiting for services or ongoing services 3. Determine the average queue length

Answer 1

Ques 2)

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