Boundary value problems in queueing theory

Cohen, J. W.

doi:10.1007/bf01189045

Cited by 94 publications

(159 citation statements)

References 13 publications

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“…However, (25)- (27) can be obtained directly from a set of differential equations instead of deriving the LST of S PS (τ), see [57,Remark 3] for an outline of how this can be done for the variance of S PS (τ), and [45,46] for higher moments. Later in this section we use similar ideas to derive differential equations for the moments of the conditional sojourn-time in the M/G/1 LCFS-NP.…”

Section: Tail Equivalence Via Conditional Momentsmentioning

confidence: 99%

“…A slightly more general model for K = 2 is the model with two parallel M/G/1 queues with service speeds depending on whether the other queue is empty or not. For general service requirement distributions, the joint distribution of the amounts of work of both classes has been obtained in [27] by solving a Wiener-Hopf problem (see [32,40] for the case of exponential service requirement distributions). The results of [27] have been exploited in [13,17,18].…”

Section: The Multi-class Casementioning

confidence: 99%

“…For general service requirement distributions, the joint distribution of the amounts of work of both classes has been obtained in [27] by solving a Wiener-Hopf problem (see [32,40] for the case of exponential service requirement distributions). The results of [27] have been exploited in [13,17,18]. In those papers, service requirements at Q 1 are either exponential or regularly varying; at Q 2 they are regularly varying.…”

Section: The Multi-class Casementioning

confidence: 99%

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The impact of the service discipline on delay asymptotics

Borst

Boxma

Núñez-Queija

et al. 2003

Performance Evaluation

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This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting-time and/or sojourn-time distribution, demonstrating that different disciplines lead to quite different tail behavior. The orientation of the paper is methodological: We outline four different methods for determining tail behavior, illustrating them for service disciplines like FCFS, Processor Sharing and LCFS.

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Section: Tail Equivalence Via Conditional Momentsmentioning

confidence: 99%

Section: The Multi-class Casementioning

confidence: 99%

Section: The Multi-class Casementioning

confidence: 99%

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The impact of the service discipline on delay asymptotics

Borst

Boxma

Núñez-Queija

et al. 2003

Performance Evaluation

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“…8) where the index k in the two products runs through 1, ... , T. Similar recurrence relations can be formulated for the coefficients Ci with i < O.…”

Section: Introductionmentioning

confidence: 86%

“…Regrettably, however, it appeared to be practically impossible to obtain more than two terms of the representation in this way. Also other analytic approaches took the generating function as a starting point which lead to interesting analytic results, but not to explicit solutions for the equilibrium distribution (compare, for instance, Cohen and Boxma [8]). Another approach would have been to exploit more directly the representation of the equilibrium distribution as a linear combination of product forms in order to obtain a more explicit expression.…”

Section: Introductionmentioning

confidence: 99%

Shortest expected delay routing for Erlang servers

Adan

Wessels

1996

Queueing Syst

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The queueing problem with a Poisson arrival stream and two identical Erlang servers is analysed for the queueing discipline based on shortest expected delay. This queueing problem may be represented as a random walk on the integer grid in the first quadrant of the plane. In the paper it is shown that the equilibrium distribution of this random walk can be written as a countable linear combination of product forms. This linear combination is constructed in a compensation procedure. In this case the compensation procedure is essentially more complicated than in other cases where the same idea was exploited. The reason for the complications is that in this case the boundary consists of several layers which in turn is caused by the fact that transitions starting in inner states are not restricted to end in neighbouring states.Good starting solutions for the compensation procedure are found by solving the shortest expected delay problem with the same service distributions but with instantaneous jockeying.It is also shown that the results can be used for an efficient computation of relevant performance criteria.

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Inter‐cell coordination in wireless data networks

Bonald

Borst

Proutière

2006

Trans Emerging Tel Tech

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International audienceOver the past few years, the design and performance of channel-aware scheduling strategies have attracted huge interest. In the present paper, we examine a somewhat different notion of scheduling, namely coordination of transmissions among base stations, which has received little attention so far. The inter-cell coordination comprises two key elements: (i) interference avoidance and (ii) load balancing. The interference avoidance involves coordinating the activity phases of interfering base stations so as to increase transmission rates. The load balancing aims at diverting traffic from heavily loaded cells to lightly loaded cells. Numerical experiments demonstrate that inter-cell scheduling may provide significant capacity gains

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Boundary value problems in queueing theory

Cited by 94 publications

References 13 publications

The impact of the service discipline on delay asymptotics

The impact of the service discipline on delay asymptotics

Shortest expected delay routing for Erlang servers

Inter‐cell coordination in wireless data networks

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