Multiservice Loss Models for Broadband Telecommunication Networks

Ross, Keith W.; Hancock, Peter

doi:10.1007/978-1-4471-2126-8

Cited by 710 publications

(458 citation statements)

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“…[1,8]. Assuming that the network parameters are changing slowly over time, the Modified Offered Load approximation, or Pointwise Stationary Approximation, that use the functional form of the equilibrium distribution, but with the time-dependent offered load obtained from analysis of a network with unlimited capacity (hence no blocking occurs) then enable using the tools of [1,8], and often provide an adequate approximation of transient blocking probabilities [3]. When the network parameters show a drastic deviation from equilibrium behaviour, however, such methods may not be adequate.…”

Section: Discussionmentioning

confidence: 99%

Transient handover blocking probabilities in road covering cellular mobile networks

Boucherie

Wal

2003

Computer Networks

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This paper investigates handover and fresh call blocking probabilities for subscribers moving along a road in a traffic jam passing through consecutive cells of a wireless network. It is observed and theoretically motivated that the handover blocking probabilities show a sharp peak in the initial part of a traffic jam roughly at the moment when the traffic jam starts covering a new cell. The theoretical motivation relates handover blocking probabilities to blocking probabilities in the M/D/C/C queue with time-varying arrival rates. We provide a numerically efficient recursion for these blocking probabilities.

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Section: Discussionmentioning

confidence: 99%

Transient handover blocking probabilities in road covering cellular mobile networks

Boucherie

Wal

2003

Computer Networks

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“…To show that the estimation procedures also apply to more elaborate loss networks, as in Ross (1995), we also considered three-link triangle networks. Direct traffic is offered to each link, but if these requests are blocked, then they can be routed on the other links if there is space.…”

Section: Loss Networkmentioning

confidence: 99%

“…The allowed model generality means that the model can be a complex loss network or resource-sharing model, perhaps with alternative routing, such as a model of a communication network; see Ross (1995). Simulations of large complex loss networks can be very time consuming, often requiring hours or more.…”

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confidence: 99%

Variance Reduction in Simulations of Loss Models

Srikant¹,

Whitt

1999

Operations Research

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We propose a new estimator of steady-state blocking probabilities for simulations of stochastic loss models that can be much more efficient than the natural estimator (ratio of losses to arrivals). The proposed estimator is a convex combination of the natural estimator and an indirect estimator based on the average number of customers in service, obtained from Little's law (L = λW). It exploits the known offered load (product of the arrival rate and the mean service time). The variance reduction is dramatic when the blocking probability is high and the service times are highly variable. The advantage of the combination estimator in this regime is partly due to the indirect estimator, which itself is much more efficient than the natural estimator in this regime, and partly due to strong correlation (most often negative) between the natural and indirect estimators. In general, when the variances of two component estimators are very different, the variance reduction from the optimal convex combination is about 1 − ρ2, where ρ is the correlation between the component estimators. For loss models, the variances of the natural and indirect estimators are very different under both light and heavy loads. The combination estimator is effective for estimating multiple blocking probabilities in loss networks with multiple traffic classes, some of which are in normal loading while others are in light and heavy loading, because the combination estimator does at least as well as either component estimator, and it provides improvement as well.

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“…Our aim is to evaluate the stationary blocking probability of an arbitrary burst and of a burst that is offered to route r. Given the difficulty in obtaining exact mathematical results for this problem, we assume as in [1], [7], [14] and [20] that each blocking event occurs independently from link to link along any route.…”

Section: The Reduced Load Fixed Point Approximationmentioning

confidence: 99%

“…The difficulties related to network models have lead OBS researchers to use a single link model that may provide crude upper bounds for the link blocking probability [14]. Furthermore, the single node analyses are limited by not considering network related issues such as the following two contrasting effects:…”

Section: Introductionmentioning

confidence: 99%