Bart Feyaerts

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.

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.

Performance Analysis of a Priority Queue with Place Reservation and General Transmission Times

In this paper, we analyze a discrete-time single-server queue with two classes of packet arrivals and a reservation-based scheduling discipline. The objective of this discipline is to give a certain priority to (delay-sensitive) packets of class 1 and at the same time to avoid packet starvation for the (delay-tolerant) packets of class 2. This is achieved by the introduction of a reserved place in the queue that can be taken by a future arrival of class 1. Both classes contain packets with generally distributed transmission times. By means of a probability generating functions approach, both the class-1 and the class-2 packet delay are studied. By some numerical examples, the delay performance of the Reservation discipline is compared to that of the classical Absolute Priority (AP) and First-In First-Out (FIFO) scheduling disciplines.

Analysis of a discrete-time queueing system with an NT-policy

In this paper, we analyse a discrete-time single-server queue operating under the NT-policy, which aims at clustering the service of customers in order to reduce the number of server activations and deactivations. Starting from an empty queue, the service of arriving customers is postponed until either of two thresholds is reached. Specifically, exhaustive service of customers is initiated only if either N customers have accumulated (space threshold) or if more than T slots have passed since the arrival of the first customer. This way, the queue cycles between three states, i.e. an empty phase, an accumulating phase and a serving phase. A Bernoulli arrival process and deterministic service times are assumed. We derive the steady-state probabilities of the systems state as well as the distributions of the phase sojourn times and the customer delay. For the latter, we condition on the phase during the customers arrival slot. The influence of the model parameters on the results is discussed by means of a numerical example.

Delay analysis of a discrete-time GI − GI − 1 queue with reservation-based priority scheduling

ABSTRACT In this paper, we study a discrete-time single-server queueing system where the arriving traffic consists of both delay-sensitive and delay-tolerant streams. We analyze the effects of a reservation-based scheduling discipline on the delay characteristics of both types of traffic. Under this discipline, a placeholder packet is inserted in the queue to accommodate future delay-sensitive arrivals, allowing them to bypass a part of the queue, without suppressing the delay-tolerant traffic. On the basis of a probability generating functions (pgf) approach, we analyze the system state distribution and the delay distribution for either traffic type and present closed-form expressions for the expected delays as well as the tail probabilities of the packet delays. We illustrate the results comparing the delay performance of our reservation-based scheduling discipline to the performance achieved by the traditional Absolute Priority (AP) and First In First Out (FIFO) disciplines.

Delay Analysis of a Queue with Reservation-Based Scheduling and Class-Dependent Service Times

In this paper, we study the delay characteristics of a discrete-time queue with a reservation-based scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays for the best-effort packets. We consider a single-server infinite-capacity queue with general independent packet arrivals of class 1 (delay-sensitive) and class 2 (best-effort). The service times of the packets are independent and have a general distribution that depends on the class of the packet. The scheduling mechanism makes use of an in-queue reserved place for future class-1 packet arrivals. A class-1 arrival takes the place of the reservation in the queue, after which a new reservation is created at the tail of the queue. Class-2 arrivals always take place at the tail of the queue. Closed-form expressions are obtained for the probability generating functions and the mean values of the packet delays of both classes.

Scheduling Announced Requests for Streamed Information

We analyse a scheduling system in which users announce requests for information from a server some time before they actually need this information. Each constituent of the requested information has its own specific deadline, which is characteristic for applications that gradually consume a stream of information (e.g., video). For that purpose, a request fully specifies when the requesting user needs each constituent of this information. Since each user device is equipped with a buffer, the server can exploit this detailed timing information to deliver parts of the requested information upfront. The more the requests are announced in advance, the better the ability of the server to avoid deadline violations. We investigate for a given server capacity via semi-analytical techniques complemented with simulations how much the requests need to be announced in advance to essentially avoid violating all deadlines.