Journal Article10.1007/BF01154549
Two-server queue with one server idle below a threshold
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TL;DR: A birth-death queueing system with two identical servers, first-come first-served discipline, and Poisson arrivals is considered, and explicit expressions are obtained for the first and second moments of the waiting and sojourn times.
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Abstract: A birth-death queueing system with two identical servers, first-come first-served discipline, and Poisson arrivals is considered Only one of the servers is active when the number of customers in the system does not exceed a prescribed threshold, whereas both are active above the threshold The problem of determining the equilibrium density of the waiting time is formulated A generating function is given for the Laplace transform of the density of the waiting time, and it is pointed out that it leads to an explicit expression for this quantity Explicit expressions are obtained for the first and second moments of the waiting and sojourn times, and they are compared with the corresponding quantities for a single-server system with the same state-dependent mean service rates
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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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Bounding of performance measures for threshold-based queuing systems: theory and application to dynamic resource management in video-on-demand servers
Leana Golubchik,J.C.S. Lui +1 more
TL;DR: The goal in this work is to develop an efficient method for computing the steady-state probabilities of a multi-server threshold-based queuing system with hysteresis, which in turn allows computation of various performance measures.
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Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms
TL;DR: This work develops an algorithm and provides an approximation scheme to obtain error bounds for the performance measures of homogeneous random walks in the quarter-plane and can be applied to the analysis of two-node queueing systems.
13
Martingale Methods for Analysing Single-Server Queues
TL;DR: A martingale method for analysing queues of M/G/1 type, which have been generalised so that the system passes through a series of phases on which the service behaviour may differ, is presented.
11
References
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.
2.6K
Diffusion approximations and models for certain congestion problems
TL;DR: In this article, the authors proposed a diffusion-based approach to the problem of traffic congestion in the context of large centralized and shared computer facilities. But this approach is not suitable for large-scale systems and is not immediately comprehensible nor useful for simple comparisons.
124
Sojourn and waiting times in a single-server system with state-dependent mean service rate
TL;DR: A birth-death queueing system with asingle server, first-come first-served discipline, Poisson arrivals and state-dependent mean service rate is considered, and a generating function is derived for the Laplace transforms of the densities of the sojourn and waiting times, leading to explicit expressions for these quantities.
7
•Book
Markov Chain Models - Rarity and Exponentiality
Julian Keilson
- 01 Jan 1979
TL;DR: In this article, the authors present an approach to Ergodicity Spectral Structure, Perron-Romanovsky-Frobenius Theorem, and a transition matrix for continuous time Markov chains.