Operations Management: An Integrated Approach, 5th Edition

SINGLE-SERVER WAITING LINE MODEL

The easiest waiting line model involves a single-server, single-line, single-phase system. The following assumptions are made when we model this environment:

1. The customers are patient (no balking, reneging, or jockeying) and come from a population that can be considered infinite.
2. Customer arrivals are described by a Poisson distribution with a mean arrival rate of λ (lambda). This means that the time between successive customer arrivals follows an exponential distribution with an average of 1/λ.
3. The customer service rate is described by a Poisson distribution with a mean service rate of μ (mu). This means that the service time for one customer follows an exponential distribution with an average of 1/μ.
4. The waiting line priority rule used is first-come, first-served.

Using these assumptions, we can calculate the operating characteristics of a waiting line system using the following formulas:

λ = mean arrival rate of customers (average number of customers arriving per unit of time)

μ = mean service rate (average number of customers that can be served per unit of time)

p = = the average utilization of the system

L_Q = = the average number of customers in the service system

L_Q = p^L = the average number of customers waiting in line

W = = the average ...