We derive formulas approximating the asymptotic variance of four estimators for the steadystate blocking probability in a multi-server loss system, exploiting diffusion process limits. These formulas can be used to predict simulation run lengths required to obtain desired statistical precision before the simulation has been run, which can aid in the design of simulation experiments. They also indicate that one estimator can be much better than another, depending on the loading. An indirect estimator based on estimating the mean occupancy is significantly more (less) efficient than a direct estimator for heavy (light) loads. A major concern is the way computational effort scales with system size. For all the estimators, the asymptotic variance tends to be inversely proportional to the system size, so that the computational effort (regarded as proportional to the product of the asymptotic variance and the arrival rate) does not grow as system size increases. Indeed, holding the blocking probability fixed, the computational effort with a good estimator decreases to 0 as the system size increases. The asymptotic variance formulas also reveal the impact of the arrival-process and service-time variability on the statistical precision. We validate these formulas by comparing them to exact numerical

this paper have been studied for the GPS policy, and for the Generalized Longest Queue First (GLQF) policy (see references in [32]). While most of these deal with the issue of computing rare buffer overflow, the similar problem for delay has been addressed in [32]. When using the effective bandwidth-type results as above, one should also keep in mind that these 16

We consider simple models of congestion control in high-speed networks and develop diffusion approximations which could be useful for resource allocation. We first show that, if the sources are ON-OFF type with exponential ON and OFF times, then, under a certain scaling, the steadystate distribution of the number of active sources can be described by a combination of two appropriately truncated and renormalized normal distributions. For the case where the source arrival process is Poisson and the service times are exponential, the steady-state distribution consists of appropriately normalized and truncated Gaussian and exponential distributions. We then consider the case where the arrival process is a general renewal process with finite coefficient of variation and service-time distributions that are phase-type and show the impact of these distributions on the steady-state distribution of the number of sources in the system. We also establish an insensitivity to service-time distributi...

A (customer) contact center is a collection of resources providing an interface between a service provider and its customers. The classical contact center is a call center, containing a collection of service representatives (reps) who talk to customers over the telephone. In a call center, the service reps are supported by quite elaborate information-and-communication-technology (ICT) equipment, such as a private branch exchange (PBX), an interactive voice response (IVR) unit, an automatic call distributor (ACD), a personal computer (PC) and assorted databases. With the rapid growth of e-commerce, contact between the service provider and its customers if often made via e-mail or the Internet instead of by telephone. Thus the general interface between a service provider and its customers is now often called a contact center. The design and management of contact centers is important, and worthy of research, because contact centers comprise a large, growing part of the economy and because they are quite complicated. Classic call centers are complicated because

We consider simple models of congestion control in high-speed networks and develop diffusion approximations which could be useful for resource allocation. We first show that, if the sources are ON-OFF type with exponential ON and OFF times, then, under a certain scaling, the steadystate distribution of the number of active sources can be described by a combination of two appropriately truncated and renormalized normal distributions. For the case where the source arrival process is Poisson and the service times are exponential, the steady-state distribution consists of appropriately normalized and truncated Gaussian and exponential distributions. We then consider the case where the arrival process is a general renewal process with finite coefficient of variation and service-time distributions that are phase-type and show the impact of these distributions on the steady-state distribution. We also establish an insensitivity to service-time distribution when the arrival process is Poisson....

In this paper, we study the impact of multiplexing real-time and best-effort sources (ATMABR, or TCP sources on the Internet) when the real-time sources are long-range dependent. We consider M=G=1 and ON-OFF models for the long-range dependent real-time sources and show that, once the long-range dependent sources reach a heavily-congested state, it takes a long time for the low-priority best-effort sources to achieve fairness. The measure of fairness we consider is the average data rate available to best-effort sources over some period of time. We study the impact of long-range dependence on this performance measure. Keywords: Long-range dependence, Self-similarity, Multimedia and broadband services, Asymptotic analysis, Tauberian theorems 1 INTRODUCTION A significant recent development in the modeling of traffic in high-speed networks is the observation that such traffic processes exhibit long-range dependence, (see, for example, [26, 19, 2, 5]). Longrange dependence in the traffic ...

This paper develops a rare-event simulation algorithm for a discrete time version of the M/G/s loss system and a related Markov modulated variant of the same loss model. The algorithm is shown to be efficient in the many server asymptotic regime in which the number of servers and the arrival rate increase to infinity in fixed proportion. A key idea is to study the system as a measure-valued Markov chain and to steer the system to the rare event through a randomization of the time horizon over which the rare event is induced. 1