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Operations Management: An Integrated Approach, 5th Edition by Nada R. Sanders, R. Dan Reid

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MULTISERVER WAITING LINE MODEL

In the single-line, multiserver, single-phase model, customers form a single line and are served by the first server available. The model assumes that there are s identical servers, the service time distribution for each server is exponential, and the mean service time is 1/μ. Using these assumptions, we can describe the operating characteristics with the following formulas:

s = the number of servers in the system

p = images the average utilization of the system

P0 = images = the probability that no customers are in the system

LQ = images = the average number of customers waiting in line

WQ = images = the average time spent waiting in line

W = WQ images = the average time spent in the system, including service

L = λW = the average number of customers in the service system

images

Note: The total service rate must be greater than the arrival rate, that is, > λ. If ≤ λ, the waiting line would ...

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