The Non-parametric Asymmetric Kernel Method in the Study of M/G/1 Queue with Optional Second Service

Authors

  • Sedda Hakmi University of Bejaia, Research Unit LaMOS, 06000 Bejaia, Algeria
  • Yasmina Djabali University of Bejaia Research Unit LaMOS, 06000 Bejaia, Algeria
  • Nabil Zougab University of Bejaia, Research Unit LaMOS, 06000 Bejaia, Algeria
  • Djamil Aïssani University of Bejaia, Research Unit LaMOS, 06000 Bejaia, Algeria

Keywords:

MG kernel, M/G/1 queue, Non-parametric density estimation, Optional service, Simulation

Abstract

This paper proposes the non-parametric asymmetric kernel method in the study of M/G/1 queue with optional second service. In this model customers arriving following a Poisson process and all demand the first service, while only some of them demand the second
service with probability p. The service times are assumed to follow a general distribution. We introduce the modified Gamma (MG) kernel method considered as a good alternative to parametric approaches such as mixture models for approximating the service and re-service time densities. Some performance measures related to this system are illustrated through simulation studies.

Downloads

Published

2026-06-02

Issue

Vol. 9 No. 2 (2026)

Section

Articles