An M/G/1 queueing model with k sequential heterogeneous service steps and vacations in the transient state. Issue 5 (3rd September 2022)

• Record Type: Journal Article
• Authors: Mohammadi, Ali; Salehi Rad, Mohammad Reza
• Is Part Of: Quality technology & quantitative management. Volume 19:Issue 5(2022)
• Page Start: 633
• Page End: 647
• Publication Date: 2022-09-03
• Subjects: M/G/1 queue -- k phase of heterogeneous service -- Bernoulli vacation -- Transient behaviour -- Laplace transform; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2021.1981529
• Languages: English
• ISSNs: 1684-3703

Abstract

ABSTRACT: This article studies a transient state M / G / 1 queueing model with k sequential heterogeneous service phase and vacations. According to a Poisson process, entrants, each arrival is serviced sequentially in k phases in the order of arrival. The service times follow a general distribution function. Upon completion of the service, the server could take a vacation with the probability θ and remain in the system to provide service to other customers with the probability 1 − θ . For this model, first, we obtain the Laplace transform of the probability generating functions. The probability generating functions of system sizes are obtained for a special case in the transient state. The mean system size is obtained by using numerical analysis. Then, the sensitivity of the model is considered.