Determining the tolerable load generated by a set of packet-based phones on a multiplexing node

Computers & Operations Research

et al. 2012

Batch servers are capable of processing batches of packets instead of individual packets. Although batch-service queueing models have been studied extensively during the past decades, the focus was mainly put on calculating performance measures related to the buffer content, whereas less attention has been paid to the packet delay. In this paper, we focus on the tail probabilities of the delay that a random packet experiences in a general batch-service queueing model. More specifically, we establish approximations for these probabilities, which are highly accurate and easy to calculate. These results, for instance, allow to accurately assess the probability that real-time packets experience an excessive delay in practical telecommunication systems.

Section: Lemma 1 If: Assumptions 1-4 Are Satisfied Then: Z C − T (Amentioning

confidence: 99%

Section: Accuracy Of the Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tail distribution of the delay in a general batch-service queueing model

Claeys

Computers & Operations Research

et al. 2012

“…For instance, the quality of service (QoS) of Voice Over IP (VoIP) conversations is generally expressed in terms of the (order of magnitude of the) probability that packets arrive too late at the end user (see e.g. [20]). The tail probabilities of the delay in a batch-service queueing model can, among others, be applied to assess the QoS of VoIP conversations in wireless personal area networks (WPANs).…”

Section: Introductionmentioning

confidence: 99%

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

Claeys

Computers & Operations Research

et al. 2013

We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model also incorporates a timer mechanism to avoid excessive delays stemming from the requirement that a service can only be initiated when the number of present customers reaches or exceeds a service threshold. The service discipline is first-come, first-served (FCFS). We demonstrate in detail that our approximations are very useful for the purpose of assessing the order of magnitude of the tail probabilities of the customer delay, except in some special cases that we discuss extensively. We also illustrate that neglecting batch-size dependent service times or a timer mechanism can lead to a devastating assessment of the tail probabilities of the customer delay, which highlights the necessity to include these features in the model. The results from this paper can, for instance, be applied to assess the quality of service (QoS) of Voice over IP (VoIP) conversations, which is typically expressed in terms of the order of magnitude of the probability of Computers & Operations Research May 1, 2013 packet loss due to excessive delays. Preprint submitted to

The N × D‐BMAP/G/1 Queueing Model: Queue Contents and Delay Analysis

Mathematical Problems in Engineering

Fiems

et al. 2011

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum.