The analysis of unreliable M[X]/G/1 queuing system with loss, vacation and two delays of verification. Issue 5 (28th May 2019)

• Record Type: Journal Article
• Authors: Saggou, Hafida; Sadeg, Ines; Ourbih-Tari, Megdouda; Bourennane, El-Bay
• Is Part Of: Communications in statistics. Volume 48:Issue 5(2019)
• Page Start: 1366
• Page End: 1381
• Publication Date: 2019-05-28
• Subjects: Batch arrivals -- Random breakdowns -- Verification time, Vacation time -- geometric loss -- Supplementary variable method; 90B22 -- 60K25 -- 68M20; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1414245
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: This paper considers an M [ X ] / G /1 queue with breakdowns, repair, Bernoulli vacation, two delays and geometric loss. In this paper, a special attention is given to the limiting distribution of system states. We obtain simplified expressions for the Probability Generating Functions (PGFs) of the joint distribution of server state and system size. Some performance measures were derived from the analysis of the steady state probabilities. PGF of a departure point system size distribution is developed. Particular cases of the studied system were investigated. The effect of system parameters on the main performance measures are illustrated and discussed.