Efficient estimation of blocking probabilities in non-stationary loss networks

This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method

Elastic calls in an integrated services network: the greater the call size variability the better the QoS

We study a telecommunications network integrating prioritized stream calls and delay tolerant elastic calls that are served with the remaining (varying) service capacity according to a processor sharing discipline. The remarkable observation is presented and analytically supported that the expected elastic call holding time is decreasing in the variability of the elastic call size distribution. As a consequence, network planning guidelines or admission control schemes that are developed based on deterministic or lightly variable elastic call sizes are likely to be conservative and inefficient, given the commonly acknowledged property of e.g.\ \textsc{www}\ documents to be heavy tailed. Application areas of the model and results include fixed \textsc{ip} or \textsc{atm} networks and mobile cellular \textsc{gsm}/\textsc{gprs} and \textsc{umts} networks. \u

The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times

Performance analysis of downlink shared channels in a UMTS network

In light of the expected growth in wireless data communications and the commonly anticipated up/downlink asymmetry, we present a performance analysis of downlink data transfer over \textsc{d}ownlink \textsc{s}hared \textsc{ch}annels (\textsc{dsch}s), arguably the most efficient \textsc{umts} transport channel for medium-to-large data transfers. It is our objective to provide qualitative insight in the different aspects that influence the data \textsc{q}uality \textsc{o}f \textsc{s}ervice (\textsc{qos}). As a most principal factor, the data traffic load affects the data \textsc{qos} in two distinct manners: {\em (i)} a heavier data traffic load implies a greater competition for \textsc{dsch} resources and thus longer transfer delays; and {\em (ii)} since each data call served on a \textsc{dsch} must maintain an \textsc{a}ssociated \textsc{d}edicated \textsc{ch}annel (\textsc{a}-\textsc{dch}) for signalling purposes, a heavier data traffic load implies a higher interference level, a higher frame error rate and thus a lower effective aggregate \textsc{dsch} throughput: {\em the greater the demand for service, the smaller the aggregate service capacity.} The latter effect is further amplified in a multicellular scenario, where a \textsc{dsch} experiences additional interference from the \textsc{dsch}s and \textsc{a}-\textsc{dch}s in surrounding cells, causing a further degradation of its effective throughput. Following an insightful two-stage performance evaluation approach, which segregates the interference aspects from the traffic dynamics, a set of numerical experiments is executed in order to demonstrate these effects and obtain qualitative insight in the impact of various system aspects on the data \textsc{qos}

Quality-of-Service differentiation in an integrated services GSM/GPRS network

We develop and analyse a generic model for performance evaluation, parameter optimisation and dimensioning in a \textsc{gsm}/\textsc{gprs} network. The model enables analytical evaluation for a scenario of integrated speech, video and data services, potentially offered in distinct priority classes. While a speech call is assigned a single traffic channel for its entire duration, both video and data calls can handle varying channel assignments. The principal distinction between these elastic call types, is that in case of video calls, a more generous channel assignment implies a better throughput and thus call quality, while for data calls the increased throughput implies a reduced sojourn time. Although a broader variety of models can be designed and analysed within the generic framework, the analytical and numerical results are presented for the \textsc{svd} model integrating speech, video and data calls, and for the \textsc{shl} model, integrating speech and two priority classes of data calls. In both models, an access queue is maintained for data calls which cannot be served immediately upon arrival. Markov chain analysis is applied to derive basic performance measures such as the expected channel utilization, service-specific blocking probabilities (\textsc{gos}), expected video \textsc{qos} (throughput) and expected (priority class-specific) data \textsc{qos} (sojourn times). Furthermore, closed-form expressions are derived for the expected video and data \textsc{qos}, conditional on the call duration or file size, respectively, and on the system state at arrival. As a potential application, these measures can be fed back to the caller as an indication of the expected \textsc{qos}. The included numerical study demonstrates the merit of the presented generic model and performance analysis, and provides \textsc{gsm}/\textsc{gprs} network operators with valuable insight in the \textsc{gos} and \textsc{qos} tradeoffs involved in balancing the various controllable system parameters

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably\ud (i) classical circuit switch telephone networks (loss networks) and\ud (ii) present-day wireless mobile networks.\ud \ud Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it has not in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hyper cubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to\ud \ud - secure upper bounds for loss probabilities and\ud - analytic error bounds for the accuracy of the approximation for various performance measures.\ud \ud The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:\ud \ud - pure loss networks as under (i)\ud - GSM-networks with fixed channel allocation as under (ii).\ud \ud The results are of practical interest for computational simplifications and, particularly, to guarantee blocking probabilities not to exceed a given threshold such as for network dimensioning.\u

An average case analysis of the minimum spanning tree heuristic for the range assignment problem

We present an average case analysis of the minimum spanning tree heuristic for the range assignment problem on a graph with power weighted edges. It is well-known that the worst-case approximation ratio of this heuristic is 2. Our analysis yields the following results: (1) In the one dimensional case ($d = 1$), where the weights of the edges are 1 with probability $p$ and 0 otherwise, the average-case approximation ratio is bounded from above by $2-p$. (2) When $d =1$ and the distance between neighboring vertices is drawn from a uniform $[0,1]$-distribution, the average approximation ratio is bounded from above by $2-2^{-\alpha}$ where $\alpha$ denotes the distance power radient. (3) In Euclidean 2-dimensional space, with distance power gradient $\alpha = 2$, the average performance ratio is bounded from above by $1 + \log 2$

Het antwoord of de vraag

Drie jaar geleden ben ik benoemd tot bijzonder hoogleraar Stochastische Processen in Telecommunicatie en Logistiek, normaal een feestelijke gebeurtenis in het leven van een wetenschapper, die voor mij op een ongelukkig moment in mijn leven plaats vond. Voor een oratie had ik op dat moment onvoldoende rust. Per 1 juni 2006 ben ik benoemd tot gewoon hoogleraar Stochastic Operations Research. Deze benoeming geeft mij de gelegenheid alsnog een uiteenzetting te geven van mijn visie op mijn vakgebied en de randvoorwaarden waaronder ik mijn werk kan, mag en wil uitvoeren. Dit komt voor mij precies op het goede moment, want zoals u weet, het leven begint bij 42, tevens het antwoord op de ‘Ultieme Vraag over het Leven, het Universum en Alles’. Wat is werkelijk van belang? Het antwoord of de vraag? Wanneer deze uitspraak voor u op dit moment cryptisch is, Geen Paniek, ik kom hierop terug. Stochastische Besliskunde is de Nederlandse naam voor Stochastic Operations Research. Stochastisch betekent waarschijnlijk (volgens Van Dale) of onzeker. Het lijkt duidelijk. Ik neem onzekere beslissingen. Dit is wellicht waar, maar slaat niet op mijn vakgebied. Bij Besliskunde zegt Van Dale: ‘op een wiskundig model gebaseerde leer die de beste beslissingen moet opleveren’. Stochastische Besliskunde is het deel van de wiskunde dat zich bezig houdt met de analyse van systemen waarin onzekerheid een rol speelt, met als doel deze systemen te optimaliseren