Queueing is an aspect of modern life that we encounter at every step in our daily activities. Whether it happens at the checkout counter in the supermarket or in accessing the Internet, the basic phenomenon of queueing arises whenever a shared facility needs to be accessed for service by a ]arge number of jobs or customers. The study of queueing is important as it gravides both a theoretical background to the kind of service that we may expect from such a facility and the way in which the facility itself may be designed to provide some specified grade of service to its customers. Our study of queueing was basically motivated by its use in the study of communication systems and computer networks. The various computers, routers and switches in such a network may be modelled as individual queues. The whole system may itself be modelled as a queueing network providing the required service to the messages, packets or cells that need to be carried. Application of queueing theory provides the theoretical framework for the design and study of such networks. The purpose of this book is to support a course on queueing systems at the senior undergraduate or graduate Ievels. Such a course would then provide the theoretical background on which a subsequent course on the performance modeHing and analysis of computer networks may be based.

An Introduction to Queueing Systems

Analysis and Application of Polling Models

We develop a performance model of a cell in a wireless communication network where the effect of handoff arrival and the use of guard channels is included. Past recursive formulas for the loss probabilities of new calls and handoff calls are developed. Monotonicity properties of the loss probabilities are proven. Algorithms to determine the optimal number of guard channels and the optimal number of channels are given. Finally, a fixed-point iteration scheme is developed in order to determine the handoff arrival rate into a cell. The uniqueness of the fixed point is shown.

Loss formulas and their application to optimization for cellular networks

A methodology is presented for analyzing a queuing submodel which frequently arises in the study of overflow models. In this submodel a finite capacity, multiserver queue with exponentially distributed service times, and arriving traffic consisting of a Poisson parcel and several overflow parcels, are assumed. By modeling the overflow parcels as interrupted Poisson processes, an exact queuing analysis is possible. The analysis yields the steady-state queue length distribution, and for each input parcel: (1) the steady-state queue length distribution at arrivals; (2) the probability that an arriving call is blocked (parcel blocking); and (3) the waiting time distribution of an arriving call, in addition to a complete characterization of the overflow due to each parcel. >

The analysis of a queue arising in overflow models

For various advantages including better utilization of radio spectrum (through frequency reuse), lower mobile transmit power requirements, and smaller and cheaper base station equipment, future wireless mobile multimedia networks are likely to adopt micro/picocellular architectures. A consequence of using small cell sizes is the increased rate of call handoffs as mobiles move between cells during the holding times of calls. In a network supporting multimedia services, the increased rate of call handoffs not only increases the signaling load on the network, but makes it very difficult for the network to guarantee the quality of service (QoS) promised to a call at setup or admission time. This paper describes an adaptive QoS handoff priority scheme which reduces the probability of call handoff failures in a mobile multimedia network with a micro/picocellular architecture. The scheme exploits the ability of most multimedia traffic types to adapt and trade off QoS with changes in the amount of bandwidth used. In this way, calls can trade QoS received for fewer handoff failures. The call level and packet level performance of the handoff scheme are studied analytically for a homogeneous network supporting a mix of wide-band and narrow-band calls. Comparisons are made to the performance of the nonpriority handoff scheme and the well-known guard-channel handoff scheme.

Adaptive quality of service handoff priority scheme for mobile multimedia networks

Teletraffic: Theory and Applications

A simple approximate formula for estimating individual call losses in overflow systems is derived using the interrupted Poisson process. The formula presents good accuracy in the single-overflow model, and it is also applicable to the multioverflow model. It is expected that the present formula is useful for the optimization of systems under given service criteria.

An Approximate Formula for Individual Call Losses in Overflow Systems

In broadband ISDN with ATM, various kinds of traffic, such as voice, data and video, share the common transmission resource. For such multiclass traffic systems, it is necessary to evaluate the grade of service (GOS) for individual traffic. In particular, for the ATM networks integrating voice and video which are of bursty property and delay sensitive, the individual performance evaluation for the mixed bursty traffic an important problem. The authors propose a simplified evaluation of the individual mean waiting time for the bursty multiclass systems appearing in the ATM network and show numerical examples for voice/video system. >

A simplified performance evaluation for bursty multiclass traffic in ATM systems

A Simplified Performance Evaluation for Packetized Voice Systems

In this paper, a simplified practical method for dimensioning asynchronous transfer mode (ATM) systems is proposed. Packet switching services are classified into two categories: connection-oriented packet switching (COPS) with quality of service (QoS) guaranteed and connection-less packet switching (CLPS) on a best effort basis. A new control scheme is proposed for maintaining the cell-level QoS requirement for the COPS even in overload conditions. A dimensioning method is also proposed for the system where the COPS is served with nonpreemptive priority over the CLPS. The methods proposed are expected to contribute to the realization of robust and economical ATM systems.

Haruo Akimaru

Papers

Teletraffic: Theory and Applications

An Approximate Formula for Individual Call Losses in Overflow Systems

A simplified performance evaluation for bursty multiclass traffic in ATM systems

A Simplified Performance Evaluation for Packetized Voice Systems

A practical dimensioning method for ATM systems