Objective:

The objective of this study is to define by means of the analysis of 2 empirical cases: the first an M/G/1 or M/D/1 system, and the second M/M/1 or M/M/S, the optimal rate of service and the economic convenience of using them or not, as well as validating two equations developed specifically to calculate the optimal number of servers.

Methodology:

Fist, the models that apply to each organization were identified, then the parameters of each system were estimated to obtain the optimal service rate, which was compared with that calculated with the equations developed for it.

Results:

For both cases, as the service/delay costs ratio increases, the optimal number of servers decreases and the cost of the system increases. Both variables were lower for the M/D/1 model than for the M/G/1, due to the strong impact of the standard deviation of the service time. Also, the cost and number of servers have been lower for the M/M/S system compared to the M/M/1, which makes it preferable in case of being able to carry out its implementation.

Study Limitations:

The parameters of each system were obtained with a limited number of data and only two organizations were studied.

Originality:

The equations developed to calculate the optimal number of servers.

Conclusions:

There are several factors that affect the behavior of the service systems. Its study allows organizations to make better decisions and develop optimization models that increase the use of their resources, the quality of their service and profitability.

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