Consider a single-server queueing system with a finite queue that can hold a maximum of 2 customers
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(a) Assume that the server must serve 2 customers simultaneously. Thus, if the server is idle when only 1 customer is in the system, the server must wait for another arrival before beginning service. Formulate the queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.
(b) Now assume that the batch size for a service is 2 only if 2 customers are in the queue when the server finishes the preceding service. Thus, if the server is idle when only 1 customer is in the system, the server must serve this single customer, and any subsequent arrivals must wait in the queue until service is completed for this customer. Formulate the result in queueing model in terms of transitions that only involve exponential distributions by defining the appropriate states and then constructing the rate diagram. Give the balance equations, but do not solve further.
Distribution
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Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
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