Abstract. Time dependent behavior has an impact on the performance of telecommunication models. Examples include: staffing a call center, pricing the inventory of private line services for profit maximization, and measuring the time lag between the peak arrivals and peak load for a system. These problems and more motivate the development of a queueing theory with time varying rates. Queueing theory as discussed in this paper is organized and presented from a communications perspective. Canonical queueing models with time-varying rates are given and the necessary mathematical tools are developed to analyze them. Finally, we illustrate the use of these models through various communication applications.

Motivated by the desire to model complex features of network traffic revealed in traffic measurements, such as heavy-tail probability distributions, long-range dependence, self similarity and nonstationarity, we propose a nonstationary offered-load model, in which connections of multiple types arrive according to independent nonhomogeneous Poisson processes, and general bandwidth stochastic processes describe the individual user bandwidth requirements at multiple links of a communication network during their connections. For example, an individual bandwidth process may be an on-off process where the on and off times have general (possibly heavy-tail) distributions. We obtain expressions for the moment generating function, mean and variance of the total required bandwidth of all customers on each link at any designated time. We suggest making decisions based on the probability that demand will exceed supply, or other designated target level, at each time of interest, using (i) numerical...

Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative real-time delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delay-history estimators to the estimator based on the queue length (QL), which requires knowledge of the mean interval between successive service completions in addition to the queue length. We characterize performance by the mean squared error (MSE). We do analysis and conduct simulations for the standard GI/M/s multi-server queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the many-server and classical heavy-traffic limiting regimes.

In the present paper, we consider a very general model of mobility, and investigate the spatial distribution of active mobile calls in the system at an arbitrary time t. We show that the set of active mobile locations forms a Poisson process in space. We consider a CDMA model with shadowing and distance-dependent path loss, and with soft handoff. We show that the set of active users in each cell (at time t) forms independent Poisson process in space. We use Campbell's Theorem to characterize the first two moments of the interference of other-cell users at each cell-site, and in this way obtain a Gaussian approximation for the other-cell interference at time t. We consider an example and use this approximation to calculate outage probabilities and compare with simulation. Our work combines the theory of Poisson processes reviewed in [3], with that of CDMA traffic modeling (see [5]). Due to the length limitation of the present paper, we do not have the opportunity here to develop the notation and theorems of Poisson

In the article, a part of a cellular mobile communication system is modelled by a queueing network of G=G=N=N stations representing each cell; the network has hexagonal structure, i.e. each G=G=N=N station is connected with six other stations. A method of diffusion approximation is used to study transient state probabilities in this model and to investigate time-dependent performances of the network. Diffusion approximation allows us to consider a large number of cells, any possible cell capacity and, unlike simulation, to obtain results even in cases where loss probabilities are very small. 1 INTRODUCTION A cellular mobile communication system is usually modelled by a network of multichannel stations, each station corresponding to a cell and the number of channels corresponding to the maximal number of connections served by the cell. Traditional modelling techniques as Markov chain approach and simulation suffer here from their usual drawbacks: state number explosion for Markovian mo...

of a Thesis Presented to The Faculty of the Department of Electrical and Computer Engineering University of Houston In Partial Fulfillment of the Requirements for the Degree Master of Science in Electrical Engineering by Kashif Shakil v Abstract In this thesis we propose a new admission control and resource reservation scheme for microcellular multimedia mobile PCS networks. This scheme takes advantage of the user to user correlation of user mobility characteristics and forms aggregate spatial flows from individual users. Spatial flows of mobile users can be utilized for making bandwidth reservation for provision of desired quality of service (QoS). The overall scheme has been designed to minimize the amount of computation required per user for its QoS demand. At the same time, our aim is to maintain an appreciable level of accuracy in admission control decisions. Furthermore, our mobility classification scheme is suitable for the periodic variations of user mobility characteristics due to time of the day and day of the week. We perform an extensive set of simulations to show that our algorithm achieves a QoS performance that is comparable to the performance of some more computationally intensive schemes. Our algorithm keeps the system resource utilization at a high level, while maintaining the QoS performance. We also show that the computational complexity of our algorithm is more than 10 times better than algorithms with comparable QoS performance. vi TABLE OF CONTENTS 1.

Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in many-server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time-varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant estimation bias in delayhistory-based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay-history estimators that effectively cope with time-varying arrival rates together with non-exponential service-time and abandonment-time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.

Motivated by interest in making delay announcements in service systems, we study real-time delay estimators in many-server service systems, both with and without customer abandonment. Our main contribution here is to consider the realistic feature of time-varying arrival rates. We focus especially on delay estimators exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant estimation bias in delayhistory-based delay estimators when the system experiences alternating periods of overload and underload. We then introduce refined delay-history estimators that effectively cope with time-varying arrival rates together with non-exponential service-time and abandonment-time distributions, which are often observed in practice. We use computer simulation to verify that our proposed estimators outperform several natural alternatives.

We develop new, improved real-time delay predictors for many-server service systems with a time-varying arrival rate, a time-varying number of servers, and customer abandonment. We develop four new predictors, two of which exploit an established deterministic fluid approximation for a many-server queueing model with those features. These delay predictors can be used to make delay announcements. We use computer simulation to show that the proposed predictors outperform previous predictors. Subject classifications: delay prediction; delay announcements; simulation; time-varying arrival rates; time-varying number of servers; nonstationary queues.