S. De Vuyst

Performance of the IEEE 802.16e Sleep Mode Mechanism in the Presence of Bidirectional Traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance.

Statistical multiplexing of correlated variable-length packet trains: an analytic performance study

We consider a statistical multiplexer which is modeled as a discrete-time single-server queueing system. Messages consisting of a variable number of fixed-length packets arrive to the muliplexer at the rate of one packet per slot (‘train arrivals’), which results in what we call a primary correlation in the packet arrival process. The distribution of the message lengths (in terms of packets) is general. Additionally, the arrival process exhibits a secondary correlation, which results from the fact that the distribution of the number of leading packet arrivals in a slot depends on some environment variable. We assume this environment to have two possible states, each with geometric sojourn times. By using generating functions and an infinite-dimensional state description, we derive closed-form expressions for the mean, the variance and the tail distribution of the buffer contents in the steady state. Some numerical examples illustrate the effect of both primary and secondary correlation on the multiplexer performance.

Place reservation: Delay analysis of a novel scheduling mechanism

We study the delay performance of a queue with a place reservation mechanism. The objective of this discipline is to provide a better quality of service to arriving packets that are delay sensitive at the cost of allowing higher delays for the best effort packets and was first proposed by Burakowski and Tarasiuk. In our model, we consider a discrete-time queue with arrivals of type 1 (delay sensitive) and type 2 (best-effort). Whenever a packet of type 1 enters the queue, it takes the position of the reservation that was created there by a previous arrival of type 1 and creates a new reservation at the end of the queue. Type 2 arrivals always take place at the end of the queue in the usual way. We present the analysis of this model based on the use of generating functions and provide results for the mean value, variance and tail behaviour of the delay experienced by both the delay-sensitive and the best-effort traffic. For a specific example, we compare the delay performance of this reservation discipline to the performance of an absolute priority discipline on the one hand, and to the reference discipline first-in first-out on the other.

Mean value and tail distribution of the message delay in statistical multiplexers with correlated train arrivals

In this paper, we study a statistical multiplexer which is modelled as a discrete-time single-server infinite-capacity queueing system. This multiplexer is fed by messages generated by an unbounded population of users. Each message consists of a generally distributed number of fixed-length packets. We assume the packet arrival process to exhibit simultaneously the following two types of correlation. First, the messages arrive to the multiplexer at the rate of one packet per slot, which results in what we call a primary correlation in the packet arrival process. Also, on a higher level, the arrival process contains an additional secondary correlation , resulting from the fact that the behaviour of the user population is governed by a two-state Markovian environment. Specifically, the state of this user environment in a particular slot determines the distribution of the number of newly generated messages in that slot. In previous work on this model, we provided analytical results for the moments and the tail distribution of the system contents. Using these results, we now concentrate on the message delay performance of this system, under the important assumption of a first-come-first-served queueing discipline for packets, whereby packets that arrive during the same slot are stored in random order. Closed-form expressions are derived for the mean value of both the total delay and the transmission time of an arbitrary message. Additionally, we provide a reasonably tight upper and lower bound for the tail probabilities of the message delay. By means of some numerical examples, we discuss the influence of the environment parameters on the delay performance.

Discrete-time buffer systems with session-based arrival streams

The paper considers a discrete-time buffer system with an infinite storage capacity and one single output channel. Users can start and end sessions during which they are active and send packets to the buffer system. In this paper we study a simple model for the resulting session-based arrival process: we assume that each active user generates a random but strictly positive number of packets per time slot. Furthermore it is assumed that the time (expressed in slots) needed to transmit a packet is geometrically distributed. The distribution of the session lengths is also geometrical. This model can be applied to study the traffic of a file server, where one file download by a user is considered to be one session. The probability generating functions of the steady-state number of active sessions, the buffer occupancy and the packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. Furthermore, an expression for the mean session delay is obtained. This allows us to study the influence of the different system parameters: some examples are presented. We end by applying the model to a web server, based on actual web traffic.

Analysis of discrete-time buffers with heterogeneous session-based arrivals and general session lengths

In this paper we study the effect of session-based arrival streams on the behavior of a discrete-time queueing system with infinite storage capacity and a single output line. These session-based arrival streams are a new and realistic approach for modelling traffic generated by users in a telecommunication network. Users from an infinite population can start and end sessions during which they are active and send packets to the queueing system. Each active user generates a random, yet strictly positive number of packets per time slot. There are T different sessions types, each characterized by their own general session-length, session-incidence and bandwidth distribution.The corresponding discrete-time queueing model is analyzed by a generating-functions approach with infinite-dimensional state description. We derive the steady-state probability generating functions of the buffer content and the packet delay. From these, we obtain the mean buffer content as well as the mean packet delay and even the mean session delay. Finally, some numerical examples illustrate the influence of various parameters on the buffer behavior.

System Content and Packet Delay in Discrete-Time Queues with Session-Based Arrivals

This paper considers a discrete-time queueing model with infinite storage capacity and one single output line. Users can start and end sessions during which they are active and send packets to the queueing system. Each active user generates a random but strictly positive number of packets per time slot: this results in a session-based arrival process of packets. This model can for instance be applied to study the traffic of a file server, where one file download by a user corresponds to one session. The steady-state probability generating functions of the number of active sessions, buffer occupancy (number of packets stored in the buffer) and packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. This allows us to study the influence of the different system parameters: some examples are presented.

Controlling the delay trade-off between packet flows using multiple reserved places

We analyse a discrete-time queueing model with packet arrivals that are either delay-sensitive (type 1) or delay-tolerant (type 2). The prominent feature of this model is its reservation-based queueing discipline, which reduces the queueing delay perceived by the 1-packets at the cost of allowing higher delays for the 2-packets. A total of N reserved places are introduced in the queue. Whenever a 1-packet enters the queue, it takes the position of the most advanced reservation and creates a new one at the end of the queue. The amount of delay differentiation between 1- and 2-packets can thus be controlled smoothly by the parameter N. We obtain the probability-generating function, the mean value and the tail distribution of the delay experienced by 1- and 2-packets.

Session Delay in File Server Output Buffers with General Session Lengths

In this paper, we analyze the delay incurred by session-based traffic in the output buffer of a file server. Users can start and end sessions during which they are active and download information from the file server. Per time slot, each active user downloads a random but strictly positive number of information packets. Each session lasts for a random, yet again, strictly positive number of slots. We model the file server output buffer as a discrete-time infinite-capacity queueing system and we present an analytical technique to study the queueing delay for sessions in case of a general session-length distribution. The analysis method is based on the combination of a generating-functions approach with the use of an infinite-dimensional state description. As a result, a closed-form expression for the mean session delay is obtained. The analysis is illustrated with a numerical example, based on real traces of file server traffic.

Fast evaluation of appointment schedules for outpatients in health care

We consider the problem of evaluating an appointment schedule for outpatients in a hospital. Given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. When a patient arrives on its appointment, the consultations of the previous patients are either already finished or are still going on, which respectively means that the physician has been standing idle or that the patient has to wait, both of which are undesirable. Optimising a schedule according to performance criteria such as patient waiting times, physician idle times, session overtime, etc. usually requires a heuristic search method involving a huge number of repeated schedule evaluations. Hence, the aim of our evaluation approach is to obtain accurate predictions as fast as possible, i.e. at a very low computational cost. This is achieved by (1) using Lindleys recursion to allow for explicit expressions and (2) choosing a discrete-time (slotted) setting to make those expression easy to compute. We assume general, possibly distinct, distributions for the patients consultation times, which allows us to account for multiple treatment types, as well as patient no-shows. The moments of waiting and idle times are obtained. For each slot, we also calculate the moments of waiting and idle time of an additional patient, should it be appointed to that slot. As we demonstrate, a graphical representation of these quantities can be used to assist a sequential scheduling strategy, as often used in practice.