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This paper deals with the queuing system M/M/1 with additional servers for a longer queue.
Clearly the traffic intensity for this system will depend on the number of additional servers. The expected
number of customers in the system, the probability of the additional of one server and the probability of
the additional of two servers are obtained under the assumption that the number of additional servers
depends on the number of customers in the system. The condition under which the M/M/1 queuing system
with additional servers is profitable is discussed. A MATLAB program is used to illustrate this condition
numerically. Finally, the maximum likelihood estimators of the parameters for this queuing system are
obtained.
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