A finite capacity queue with Markovian arrivals and two servers with group services. (1994)

• Record Type: Journal Article
• Authors: Chakravarthy, S.; Alfa, Attahiru Sule
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 2(1994)
• Page Start: 161
• Page End: 178
• Publication Date: 1994
• Subjects: queues -- renewal process -- finite capacity -- Markovian arrival process -- Laplace-Stieltjes transform -- algorithmic probability; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000171
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting time distribution is shown to be of phase type when the interarrival times are of phase type. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures are discussed. A conjecture on the nature of the mean waiting time is proposed. Some illustrative numerical examples are presented.