Bart Steyaert

Performance analysis of a single-server ATM queue with a priority scheduling

In this paper, we consider a discrete-time queueing system with head-of-line priority. First, we will give some general results on a GI-1-1 queue with priority scheduling. In particular, we will derive expressions for the probability generating function of the system contents and the cell delay. Some performance measures (such as mean, variance and approximate tail distributions) of these quantities will be derived, and used to illustrate the impact and significance of priority scheduling in an ATM output queueing switch.

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

Abstract In this paper we consider a discrete-time queueing model, useful for the design and the performance evaluation of many slotted communication system in general, and ATM-based networks in particular. The model assumes a general independent packet arrival process, an infinite waiting room, and an arbitrary number of servers. By means of an approximation technique, explicit closed-form expressions are derived for the tail probabilities of both the buffer contents (queue length) and the delay (or the waiting time). These formulas are very easy to evaluate. They are applied in the performance analysis of an ATM switching element with output queueing, in order to obtain predictions for such quantities as the cell loss ratio and the delay jitter. Also, an application with more bursty arrivals is discussed. In both cases, very good agreement between actual (numerical) and approximate (analytic) results is observed.

Delay characteristics in discrete-time GI-G-1 queues with non-preemptive priority queueing discipline

Priority scheduling for packets is becoming a hot topic, as attempts are being made to integrate voice services in existing data networks. In this paper, we consider a discrete-time queueing system with head-of-line (HOL) non-preemptive priority scheduling. Two classes of traffic will be considered, i.e., high-priority and low-priority traffic, which both generate variable-length packets. We will derive expressions for the probability generating function of the packet delay of the high-priority traffic and the low-priority traffic. From these, some performance measures (such as the mean value) will be derived. These will be used to illustrate the significance of priority scheduling and will be applied to an output queueing switch.

Discrete-time queues with generally distributed service times and renewal-type server interruptions

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions. Server interruptions are modeled as an on/off process with geometrically distributed on-periods and generally distributed off-periods. As message lengths can exceed one time-slot, different operation modes are considered, depending on whether service of an interrupted message continues, partially restarts or completely restarts after an interruption. For all alternatives, we establish expressions for the steady-state probability generating functions (pgf) of the buffer contents at message departure times and random slot boundaries, of the unfinished work at random slot boundaries, the message delay, and the lengths of the idle and busy periods. From these results, closed-form expressions for various performance measures, such as mean and variance of the buffer occupancy and message delay, can be established. As an application, we show that this model is able to assess performance of a multi-class priority scheduling system. We then illustrate our approach with some numerical examples.

Analysis of a discrete-time GI-G-1 queueing model subjected to bursty interruptions

In this contribution, we investigate a discrete-time single-server queue subjected to server interruptions generated by a 2-state Markov process. The model under consideration assumes customers with multiple-slot service times, which leads to the introduction of two different service strategies depending on whether service of an interrupted customer continues or restarts after an interruption. For both alternatives, we establish expressions for the steady-state probability generating functions of the buffer contents, the unfinished work and the customer delay in terms of the effective customer service times. From these results, closed-form expressions for various performance measures, such as the moments of these quantities, can be established. After dealing with some stability issues, we illustrate the impact of both service strategies on the buffer performance with some numerical examples.

Randomly Interrupted GI-G-1 Queues Service Strategies and Stability Issues

We consider a discrete-time queueing system subjected to random server interruptions. As customers arriving in the queue require generally distributed service times, the server can be interrupted during a customers service. Therefore, nine different service strategies are proposed and analyzed using a probability generating functions approach. Performance measures under investigation include moments of steady-state buffer contents at random slot boundaries in equilibrium and moments of the customer delay. In particular we focus on the stability requirements for the strategies under consideration.

Deriving delay characteristics from queue length statistics in discrete-time queues with multiple servers

Abstract In this paper, we investigate a discrete-time multiserver buffer system. Packets arrive in the system according to a general, possibly correlated, process, which is not further specified. The service times of the packets are of constant length. Explicit expressions are derived for the distribution, probability generating function, mean and variance of the packet delay, in terms of the distribution, probability generating function, mean and variance of the buffer contents. It is observed that knowledge of the exact nature of the arrival process is not required in order to be able to derive these (general) relationships between the statistics of the delay and the occupancy.

An effective algorithm to calculate the distribution of the buffer contents and the packet delay in a multiplexer with bursty sources

A statistical multiplexer with a finite number of independent and identical bursty traffic sources (users) is considered. The burstiness of the sources is modeled by describing both the active periods (during which a user generates one packet per slot) and the passive periods (during which a user does not generate any data) as geometric random variables. As a result, a correlated-arrivals queuing model for the multiplexer buffer is obtained, and it is analyzed by numerical means. Specifically, algorithms are given for the explicit derivation of the probability mass functions of the buffer contents (in packets) and the packet delay (in slots). The results indicate a very strong influence of the burstiness of the required buffer space in the multiplexer and the possible values of the packet delay, even for a given mean arrival rate per slot.<<ETX>>

Analysis of a discrete-time preemptive resume priority buffer

In this paper, we analyze a discrete-time preemptive resume priority queue. We consider two classes of customers which have to be served, where customers of one class have preemptive resume priority over customers of the other. Both classes contain customers with generally distributed service times. We show that the use of probability generating functions is beneficial for analyzing the system contents and customer delays of both classes. It is shown (theoretically as well as by some practical procedures) how moments and approximate tail probabilities of system contents and customer delays are calculated. The influence of the priority scheduling discipline and the service time distributions on the performance measures is shown by some numerical examples.

Analysis of a versatile batch-service queueing model with correlation in the arrival process

In the past, many researchers have analyzed queueing models with batch service. In such models, the server typically postpones service until the number of present customers reaches a service threshold, whereupon service is initiated of a batch consisting of several customers. In addition, correlation in the customer arrival process has been studied for many different queueing models. However, correlated arrivals in batch-service models have attracted only modest attention. In this paper, we analyze a discrete-time D-BMAP/G^l^,^c/1 queue, whereby the service time of a batch is dependent on the number of customers within it. In addition, a timing mechanism is included, to avoid that customers suffer excessive waiting times because their service is postponed until the amount of customers reaches the service threshold. We deduce various useful performance measures related to the buffer content and we investigate the impact of the traffic parameters on the system performance through some numerical examples. We show that correlation merely has a small impact on the service threshold that minimizes the mean system content, and consequently, that the existing results of the corresponding independent system can be applied to determine a near-optimal service threshold policy, which is an important finding for practitioners. On the other hand, we demonstrate that for other purposes, such as performance evaluation and buffer management, correlation in the arrival process cannot be ignored, a conclusion that runs along the same lines as in queueing models without batch service.