Consider a single-server queueing system that can hold a maximum of two customers excluding those being served. Theserver serves customers only in batches of two, and the service time (for a batch) has an exponential distribution with amean of 1 unit of time. Thus if the server is idle and there is only one customer in the system, then the server must waitfor another arrival before beginning service. The customers arrive according to a Poisson process at a mean rate of 1 perunit of time.(1). Draw the rate diagram. (Hint: think about how the state will change after one service completion.)(2). Setup the rate balance equations. (Hint: use the rate balance equations 1.)(3). Compute pn and L.(4). Compute the actual mean arrival rate Ā.

Problem SetupServer can hold a maximum of 2 customers in queue (excluding the batch in…

Answered: Consider a single-server queueing…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Suppose we have a small call center staffed by two operators A and B handling three telephone lines. A only handles line 1, and B only handles only line 2 and 3. Calls arrive according to a Poisson process with rate A = 100 calls per hour. All arrivals prefer line 1. Arrivals find all lines are busy will go away. Service times are exponentially distributed with a mean of 4 minutes. Customers are willing to wait an exponentially distributed length of time with a mean of 8 minutes before reneging if service has not begun. Describe a continuous time Markov chain to model the system and give the rate transition diagram and the generator G.
A car servicing station has 2 bays where service can be offered simultaneously. Because of space limitation, only 4 cars are accepted for servicing. The arrival pattern is Poisson with 12 cars per day. The service time in both the bays is exponentially distributed with µ = 8 cars per day per bay. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system.
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