Book Chapter10.1016/S0927-0507(05)80174-4
Chapter 10 Queueing theory
Robert B. Cooper
- 01 Jan 1990
- Vol. 2, pp 469-518
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TL;DR: This chapter discusses the queueing theory, which concerns the construction and analysis of mathematical models of systems that provide service to customers whose arrival times and service requirements are random.
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Abstract: Publisher Summary This chapter discusses the queueing theory Queueing theory concerns the construction and analysis of mathematical models of systems that provide service to customers whose arrival times and service requirements are random The basic queueing model, from which more complicated models can be constructed, consists of three components: (1) the input process, (2) the service mechanism, and (3) the queue discipline The input process describes the statistical properties of the time instants (epochs) at which the customers arrive Typically, this is expressed in terms of the distribution of the inter-arrival times, but other descriptions may be preferable, depending on context Similarly, the service mechanism specifies the number of servers and describes the statistical properties of the service times Usually, the service times are assumed to be independent of the arrival process and each other, and to be identically distributed, without regard for which serverprovides the service The queue discipline describes the behavior of the customers who are blocked—that is, who find all servers busy when they arrive Two typical assumptions for the queue discipline are (1) all blocked customers leave immediately, or (2) all blocked customers wait in a queue until they are served; in the latter case it may be necessary to specify the order in which waiting customers are selected from the queue, such as first-in first-out (FIFO) or its reverse, last-in first-out (LIFO)
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Citations
Fundamentals of Queueing Theory
Rodney Coleman
- 01 May 1975
TL;DR: The Fundamentals of Queueing Theory, Fourth Edition as discussed by the authors provides a comprehensive overview of simple and more advanced queuing models, with a self-contained presentation of key concepts and formulae.
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Reconfiguration of inpatient services to reduce bed pressure in hospitals
Navid Izady,Bahar Arabzadeh,Nicholas Sands,James Adams +3 more
TL;DR: This study proposes a cost-effective methodology to reconfigure inpatient services and reduce bed pressure in hospitals, using novel approximations and heuristic search algorithms, resulting in significant savings and improved patient outcomes.
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Waiting times in discrete-time cyclic-service systems
Onno Boxma,W.P. Groenendijk +1 more
- 01 Jan 1987
TL;DR: In this paper, a decomposition for the amount of work in such systems is obtained, leading to an exact expression for a weighted sum of the mean waiting times at the various queues.
5
Estimating Effective Capacity in Erlang Loss Systems under Competition
TL;DR: An Erlang loss system with two streams of arriving customers, where arrival rates vary by time-of-day is considered, and a maximum likelihood estimator is constructed that makes good use of the data, but is slow to evaluate.
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References
A queue with starter and a queue with vacations: delay analysis by decomposition
Hanoch Levy,Leonard Kleinrock +1 more
TL;DR: This paper analyzes both a queueing system that incurs a start-up delay whenever an idle period ends and one in which the server takes vacation periods, and shows that the delay distribution in the queue with starter is composed of the direct sum of two independent variables.
81
Some New Results for the M/M/1 Queue
TL;DR: New results are obtained for the single server queue with Poisson arrivals and exponential service times and a closed form solution involving only finite sums is obtained.
74
Matrix-analytic methods in queuing theory☆
TL;DR: The author argues the case for an algorithmic optic on the problems of applied probability, sketches the main steps in the construction of computer codes for the evaluation of stationary distributions of interest, and builds on certain nonlinear matrix equations that arise naturally in the study of structured Markov chains.
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