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Detailed schedule
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Show all the abstracts
Show all the abstracts
Thursday 11:00:00 Timetabling in education and sport
Room 126 - Chair: G. Vanden Berghe
Thursday 11:00:00 Transportation management
Room 130 - Chair: F. Semet
Thursday 11:00:00 Networks
Room 138 - Chair: B. Fortz
Thursday 11:00:00 Nonconvex optimization 1
Room 035 - Chair: F. Bach
Thursday 14:00:00 Constraint programming models 1
Room 126 - Chair: Y. Deville
Thursday 14:00:00 Vehicle routing
Room 130 - Chair: S. Limbourg
Thursday 14:00:00 Combinatorial optimization and IP applications
Room 138 - Chair: Q. Louveaux
Thursday 14:00:00 Nonconvex Optimization 2
Room 035 - Chair: R. Sepulchre
Thursday 16:10:00 Constraint programming models 2
Room 126 - Chair: P. Schaus
Thursday 16:10:00 Performance modeling
Room 130 - Chair: G. Janssens
Thursday 16:10:00 Scheduling
Room 138 - Chair: K. Sorensen
Thursday 16:10:00 Planning under uncertainty
Room 035 - Chair: R. Leus
Friday 09:00:00 Metaheuristics
Room 126 - Chair: J. Teghem
Friday 09:25:00 Production and distribution (9:25)
Room 130 - Chair: Y. Arda
Friday 09:00:00 Multiple criteria
Room 138 - Chair: R. Bisdorff
Friday 09:25:00 Stochastic models (9:25)
Room 035 - Chair: L. Esch
Friday 11:00:00 Constraint programming and Supply Chain Management
Room 126 - Chair: Y. Deville
Friday 11:00:00 OR in health management
Room 130 - Chair: P. De Causmaecker
Friday 11:00:00 Rankings and importance indices
Room 138 - Chair: JL. Marichal
Friday 11:00:00 Queueing
Room 035 - Chair: S. Wittevrongel
- Modelling data traffic performance in file servers: session-based arrivals
Bart Feyaerts (Ghent University)
Co-authors: Stijn De Vuyst, Sabine Wittevrongel, Herwig Bruneel
Abstract:
Abstract
Contemporary communication networks are faced with increasingly heterogeneous traffic characteristics. In order to get reliable predictions about the network performance, adequate models for both data traffic and network components are indispensable. In this paper we focus on the session-based arrival process, a novel model for data traffic. This model considers users that can start and end sessions, during which data are transported over the network. We then use the model to obtain analytical and numerical results for the mean delay of a session in a network buffer.
1 Introduction
Packet buffers are crucial components in many communication networks, where they provide for temporary storage of data packets. A sound understanding of these buffers and how they behave, is therefore crucial to study the network performance as a whole. An essential factor of the performance measures of a packet buffer, is the nature of the arrival process that generates the data packets. Session-based arrival streams form a new approach for modelling data traffic in modern communication networks. Users from an infinite population can start and end sessions, during which data are sent over the network.
In this paper, we focus on a packet buffer, modelled as a discrete-time, single-server queueing system with infinite buffer capacity, geometric service times and session-based arrivals. Per time slot, each of the sessions generates a random but strictly positive number of information packets. The sessions all last for a random, but yet again, strictly positive number of time slots. This session-based packet generation scheme counts as a generalization of the train arrival process, where sessions (in this context referred to as messages) have a fixed bandwidth of 1 packet per slot.
All data traffic arriving to the buffer can be divided into an arbitrary number T of session types. Each of these session types is characterized by three stochastic components. The session generation process of a particular type describes the number of new sessions of that type during a random slot. The session bandwidth denotes the number of packets generated by a session during a random slot. Finally, the session length corresponds to the number of slots a session lasts.
2 Description of the analysis
In previous work [1], a Markovian system state description with an infinite-length system state vector was constructed. This vector contains the buffer content at the end of a certain slot and for each session type, the number of active sessions during that slot, grouped by the amount of slots the sessions are already active. Also the steady-state probability generating function of this system state vector has been obtained, as well as analytical expressions for the mean buffer content and the mean packet delay.
Based on these preliminary results, we now investigate the mean value of the session delay. The delay of a session is defined as the integer number of slots, starting at the end of the slot in which the session's first packet arrives to the buffer, until the end of the slot in which the session's final packet leaves the system. The first step is then to obtain the mean session delay of sessions of a given type and length. This derivation is very different for single-slot and multiple-slot sessions. In the next step we produce the mean session delay of sessions of a given type by taking the sum of the conditional means obtained in the former step, weighted over the corresponding session length probability. In the final step, an analogous weighted sum yields the overall mean session delay.
Numerical examples show both some intuitive and some more intriguing results. As expected, an increasing system load leads to an increasing mean session delay; this result is also obtained for an increasing variance in the arrival process. A more counterintuitive result is that the mean session delay can be smaller than the mean packet delay for some configurations. This can occur when there is unbalanced traffic: frequent few-packet sessions in combination with unfrequent many-packet sessions where the major part of the packets arrive during the unfrequent sessions. Although these unfrequent sessions have little effect on the mean session delay, they have a crucial effect on the mean packet delay.
3 Application
A possible application of our model is to study the behaviour of the output buffer of a file server. Considering each file transfer as a single session, the traffic to such an output buffer can be well described by our session-based model. Since the model allows for general distributions of both the session lengths and the session bandwidths, it enables us to take into account actual traffic characteristics, as observed from a real traffic trace.
References
[1] S. Wittevrongel, S. De Vuyst and H. Bruneel, Analysis of discrete-time buffers with general session-based arrivals, Proceedings of ASMTA 2009 (Madrid, June 2009), Lecture Notes in Computer Science, 2009, vol. 5513, pp. 189-203.
- Generalization of preemptive and non-preemptive priority queues
Joris Walraevens (Ghent University - UGent)
Co-authors: Tom Maertens. Herwig Bruneel
- Queueing analysis of outpatient scheduling in health care
Stijn De Vuyst (Ghent University)
Co-authors: Dieter Fiems (first author), Stijn De Vuyst, Herwig Bruneel.
- Stochastic Hybrid Simulation
Ben Lauwens (Royal Military Academy)
Friday 15:10:00 Optimization software
Room 126 - Chair: E. Loute
Friday 15:10:00 Integrated operations planning
Room 130 - Chair: B. Raa
Friday 15:10:00 Cycles in graphs
Room 138 - Chair: F. Spieksma
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