Behavior Analysis of an M/M/1 vacation Queue in Random Environment. Issue 4 (4th July 2021)

• Record Type: Journal Article
• Authors: Ammar, Sherif
• Is Part Of: Quality technology & quantitative management. Volume 18:Issue 4(2021)
• Page Start: 397
• Page End: 417
• Publication Date: 2021-07-04
• Subjects: Single server queue -- vacation -- random environment -- generating functions -- transient analysis; 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: 10.1080/16843703.2020.1846268
• Languages: English
• ISSNs: 1684-3703

Abstract

ABSTRACT: This study examines an M/M/1 vacation queue in a random environment. This system is considered a classical M / M / 1 queueing system in which customers are served one by one in the operative phase i, i = 1, 2, …, n, and the arrival and service rates are λ i and μ i ., respectively. The system starts the vacation phase when it is empty and there are no customers to which to provide the service. Furthermore, the system moves to some operating phase i with probability q i, i = 1, 2, …, n at the end of the vacation phase. Based on the generating function technique, we derived the transient probabilities and some performance measures. The steady-state analysis is also discussed. Finally, the effectiveness of the proposed system parameters on the behaviour of the system is illustrated with some numerical examples.