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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.

This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily single-node) queues with Markov modulation, two variants were distinguished: one in which the server speed is modulated, and one in which the service requirement is modulated (i.e., depends on the state of the background process upon arrival). The setup of the present paper, however, is more general, as we allow both the server speed and the service requirement to depend on the background process. For this model we derive a Functional Central Limit Theorem: we show that, after accelerating the arrival processes and the background process, a centered and normalized version of the network population vector converges to a multivariate Ornstein-Uhlenbeck process. The proof of this result relies on expressing the queueing process in terms of Poisson processes with a random time change, an application of the Martingale Central Limit Theorem, and continuous-mapping arguments.

The diversity of multimedia-enabled devices supporting streamed multimedia is ever growing. Multicast delivery of TV channels in IP networks to a heterogeneous set of clients can be organised in many different ways, which brings up the discussion which one is optimal. Scalable video streaming has been believed to be more efficient in terms of network capacity utilisation than simulcast video delivery because one flow can serve all terminals, while with simulcast all resolutions are offered in parallel. At the same time, it is also largely recognised that in order to provide the same video quality compared to non-layered video coding, scalable video coding (SVC) incurs a bit rate penalty.In this paper we compare simulcast and SVC in terms of their required capacity in an IPTV network scenario where a bouquet of TV channels is offered to the subscribers. We develop methods to calculate and approximate the capacity demand for two different subscriber behaviour models. These methods are then used to explore the influence of various parameters: the SVC bit rate penalty, the number of offered channels, the channel popularity and the number of subscribers. The main contribution of this paper is that we derive an analytical formula to calculate the SVC limit bit rate penalty beyond which SVC is less efficient than simulcast. In the realistic IPTV examples considered here, the limit is found to lie between 16% and 20%, while the reported values for this coding penalty range from 10% up to 30% for current H.264 SVC codecs, indicating that SVC in IPTV is not always more efficient than simulcast.

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We analyze a discrete-time priority queue with train arrivals. Messages of a variable number of fixed-length packets belonging to two classes arrive to the queue at the rate of one packet per slot. We assume geometrically distributed message lengths. Packets of the first class have transmission priority over the packets of the other class. By using probability generating functions, some performance measures such as the moments of the packet delay are calculated. The impact of the priority scheduling discipline and the correlation in the arrival process is shown by some numerical examples.

Abstract-We propose a discrete-time queueing model for the evaluation of the IEEE 802.16e sleep-mode mechanism of Power Saving Class (PSC) I in wireless access networks. Contrary to previous studies, we model the downlink traffic by means of a Discrete Batch Markov Arrival Process (D-BMAP) with phases, which allows to take traffic correlation into account. The tradeoff between energy saving and increased packet delay is discussed. In many situations, the sleep-mode performance improves for heavily correlated traffic. Also, when compared to other strategies, the exponential sleep-period update strategy of PSC I may not always be the best.Index Terms-Discrete-time queueing model, sleep mode, IEEE 802.16e, analytic study.

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays