Title: Maximum likelihood estimates in an M/M/c queue with heterogeneous servers

Authors: Sarat Kumar Acharya; Sara Verónica Rodríguez-Sánchez; César Emilio Villarreal-Rodríguez

Addresses: Departament of Statistics, Sambalpur University, Jyoto Vihar-768019, Sambalpur, Orissa, India ' Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León (UANL), A.P. 111-F, Ciudad Universitaria, 66455 San Nicolás de los Garza, N.L., Mexico ' Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León (UANL), A.P. 66-F, Ciudad Universitaria, 66455 San Nicolás de los Garza, N.L., Mexico

Abstract: This paper presents the derivation of maximum likelihood estimates for the arrival rate and service rates in a stationary M/M/c queue with heterogeneous servers. Although previous works facing the problem can be found in the literature, all of them are only valid under the assumption of transferring of customers in service. A more realistic approach for many systems is developed in this paper. This model considers the customers are attended by the available faster server and there is no transfer of customers among servers. The model can be applied in a large variety of systems such as production systems, banking, cyber café or taxi station.

Keywords: queueing systems; heterogeneous servers; maximum likelihood estimates; MLE; equilibrium; stationary M/M/c queues; arrival rate; service rate.

DOI: 10.1504/IJMOR.2013.054735

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.4, pp.537 - 549

Received: 22 Jun 2012
Accepted: 10 Aug 2012
Published online: 31 Mar 2014 *

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