Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues

Bruneel, Herwig; Steyaert, Bart; Desmet, E.; Petit, Guido H.

doi:10.1016/0377-2217(94)90287-9

Cited by 57 publications

(42 citation statements)

References 16 publications

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“…This is widely used to calculate the probability mass function from probability generating functions [9] and even more frequently in combinatorics [12]. However, it does not seem to be used yet in case of the analysis of the transient behavior of queues.…”

Section: Approximation Of the Sequencementioning

confidence: 99%

Using Singularity Analysis to Approximate Transient Characteristics in Queueing Systems

Walraevens¹,

Fiems²,

Moeneclaey³

2009

Prob. Eng. Inf. Sci.

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In this paper, we develop a simple method to approximate the transient behavior of queueing systems. In particular, it is shown how singularity analysis of a known generating function of a transient sequence of some performance measure leads to an approximation of this sequence. To illustrate our approach, several specific transient sequences are investigated in detail. By means of some numerical examples, we validate our approximations and demonstrate the usefulness of the technique.

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Section: Approximation Of the Sequencementioning

confidence: 99%

Using Singularity Analysis to Approximate Transient Characteristics in Queueing Systems

Walraevens¹,

Fiems²,

Moeneclaey³

2009

Prob. Eng. Inf. Sci.

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“…The mean of the delay d of an arbitrary packet (regardless of type) can therefore immediately be obtained from (7). For a 2-class system, this can be written as…”

Section: Theorem 1 (Reservation Theorem)mentioning

confidence: 99%

“…We use the dominant pole approximation which is known to yield very accurate results, see e.g. [5,7]. Specifically, from the inversion formula for z-transforms, it follows that the probability mass function Prob[d 1 = n] can be expressed as a weighted sum of negative nth powers of the poles of D 1 (z).…”

Section: Tail Distribution Of the Type-1 Packet Delaymentioning

confidence: 99%

Transform-Domain Analysis of Packet Delay in Network Nodes with QoS-Aware Scheduling

Vuyst

Wittevrongel

Bruneel

2011

Network Performance Engineering

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Abstract. In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1.

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“…[27]). We will use here the technique presented in [15] and [28] to derive the tail distribution of the system contents. Specifically, we have that for sufficiently large values of N , the tail distribution of the system contents can be approximated as…”

Section: Tail Probabilities Of the System Contentsmentioning

confidence: 99%

“…To the best of our knowledge, in most of the existing literature on discrete-time multiserver queueing models, the service (or transmission) times of customers (or packets) are assumed to be constant, equal to one slot (see [12]- [15]) or multiple slots ( [16]). These assumptions are appropriate when modeling for instance buffers in ATM-based integrated-services digital networks, in view of the fixed packet (cell) length used in these networks ( [17]).…”

Section: Introductionmentioning

confidence: 99%

Discrete-time multiserver queues with geometric service times

Gao

Wittevrongel

Bruneel

2004

Computers & Operations Research

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Scope and purposeDiscrete-time queueing models are widely used to study the behavior of various types of telecommunication and computer systems. Most of the existing studies of discrete-time multiserver queueing models assume that the service times of the customers are constant.Recently, however, there has been an increased interest in discrete-time models with nondeterministic service times, due to the more and more complicated and irregular service mechanisms in nowadays telecommunication networks. In view of this, this paper focuses on a discrete-time queueing system with multiple servers and geometrically distributed service In this paper, a discrete-time multiserver queueing system with infinite buffer size and general independent arrivals is considered. The service times of a packet served by one of the servers are assumed to be independent and identically distributed according to a geometric distribution. Each packet gets service from only one server. In the paper, the behavior of the queueing system is studied analytically by means of a generating-functions approach.This results in closed-form expressions for the mean values, the variances and the tail distributions of the system contents and the packet delay. Some numerical examples are given to illustrate the analysis.

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Analytic derivation of tail probabilities for queue lengths and waiting times in ATM multiserver queues

Cited by 57 publications

References 16 publications

Using Singularity Analysis to Approximate Transient Characteristics in Queueing Systems

Using Singularity Analysis to Approximate Transient Characteristics in Queueing Systems

Transform-Domain Analysis of Packet Delay in Network Nodes with QoS-Aware Scheduling

Discrete-time multiserver queues with geometric service times

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