Journal ArticleDOI
An M/G/1 queue with second optional service
TLDR
The well-known Pollaczec–Khinchine formula and some other known results including M/D/1, M/Ek/1 and M/M/1 have been derived as particular cases.Abstract:
We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate l (>0) all demand the first ‘essential’ service, whereas only some of them demand the second ‘optional’ service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B(v) and that of the second optional service are exponential with mean service time 1/m_2 (m_2>0). The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly. The well-known Pollaczec–Khinchine formula and some other known results including M/D/1, M/E_{k}/1} and M/M/1 have been derived as particular cases.read more
Citations
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Journal ArticleDOI
An M/G/1 queue with second optional service
TL;DR: The well-known Pollaczec–Khinchine formula and some other known results including M/D/1, M/Ek/1 and M/M/1 have been derived as particular cases.
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Travel time estimation and order batching in a 2-block warehouse
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References
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Book
The single server queue
Clifford W. Marshall,Jacob Cohen +1 more
TL;DR: In this paper, the basic models of queueing theory are described and a dual aim is to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.
Journal ArticleDOI
The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
TL;DR: In this paper, it is shown that certain stochastic processes with discrete states in continuous time can be converted into Markov processes by the well-known method of including supplementary variables, and conditions under which it is possible to obtain a solution for arbitrary distributions are examined.
Journal ArticleDOI
The Single Server Queue
TL;DR: In this paper, the basic models of queueing theory are described and a dual aim is to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.