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 = 
the average utilization of the system
P0 = 
= the probability that no customers are in the system
LQ = 
= the average number of customers waiting in line
WQ = 
= the average time spent waiting in line
W = WQ 
= the average time spent in the system, including service
L = λW = the average number of customers in the service system
Note: The total service rate must be greater than the arrival rate, that is, sμ > λ. If sμ ≤ λ, the waiting line would ...
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