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Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots |
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| Affiliation: | 1. Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal;2. Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston Ont., Canada K7K 7B4;3. Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India;1. Department of Mathematics, Visva-Bharati University, Siksha-Bhavana (Institute of Science), Santiniketan, West Bengal 731235, India;2. Mathematics Department, Ananda Mohan College, Kolkata, West Bengal 700009, India;1. Business School, Sichuan University, Chengdu 610064, PR China;2. Decision Sciences Department, LeBow College of Business, Drexel University, Philadelphia, PA 19104, USA;3. Sichuan Institute of Building Research, Chengdu 610064, PR China |
| Abstract: | This paper presents a simple closed-form analysis for evaluating system-length distributions at various epochs of the discrete-time GI/D-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at prearrival epochs. We provide the steady-state system-length distribution at random epoch by using the classical argument based on Markov renewal theory. The queueing-time distribution has also been investigated. Numerical aspects have been tested for a variety of interarrival- and service-time distributions and a sample of numerical outputs is presented. |
| Keywords: | Discrete-time Markovian service process (D-MSP) Queueing-time Roots System-length |
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