Jerry Place

Approximation models of wireless cellular networks using moment matching

In this paper we present an analytical model for micro- and pico-cell wireless networks for any arbitrary topology in a high mobility feedforward environment. We introduce an approximation technique which uses a single-cell decomposition analysis which incorporates moment matching of handoff processes into the cell. The approximation technique can provide close approximations for non-Poisson arrival traffic and it is easily parallelized. Performance measures such as new calls blocked, handoff calls lost, and forced termination are derived for any general independent call arrival distribution in a heterogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.

Correlation properties of the token leaky bucket departure process

In this paper we focus on the behavior of the leaky bucket mechanism with respect to second-order statistics of the departure process under various correlated cell arrival and deterministic token arrival distributions. We derive expressions for the lag-k auto-correlation of the inter-departure times for the leaky bucket cell departure stream and we produce numerical examples for the lag-k auto-correlation of the leaky bucket inter-departure times for several different cell arrival distributions exhibiting both positive and negative auto-correlations.

An efficient algorithm for mutual exclusion using queue migration in computer networks

A nonsymmetric deadlock-free mutual exclusion algorithm for computer networks is presented. The algorithm requires O(m) messages to synchronize m modes in a lightly loaded system, and the performance approaches a constant k dependent on m as the workload increases. In a medium to heavily loaded system, it outperforms other proposed algorithms and its performance is independent of network topology. >

Generating matrix exponential random variates

In this paper we present a technique for generating random variates from an empirical distribution using the matrix exponential representation of the distribution. In our experience, a matrix exponential representation of an empirical distribution produces random variates with an excellent fit with the empirical distribution. This technique is particularly important when the empirical data is very bursty, i.e., has a high variance. In this paper we discuss how to find the matrix exponential representation of an empirical distribution and we present our technique for generating random variates from the empirical distribution using its matrix exponential representation. We show how the matrix exponential representation of an empirical distribution is found through an example and then we show that matrix exponential random variates are an excellent fit with the empirical data through an χ2 goodness-of-fit test.

Generating correlated matrix exponential random variables

In this paper, we focus on inter-arrival time autocorrelation and its impact on model performance. We present a technique to generate matrix exponential random variables that match first-order statistics (moments) and second-order statistics (autocorrelation) from an empirical distribution. We briefly explain the matrix exponential distribution and show that we can represent any empirical distribution arbitrarily closely as matrix exponential. We then show how we can incorporate an autocorrelation structure into our matrix exponential random variables using the autoregressive to anything technique. We present examples showing how we match first and second-order statistics from empirical distributions and finally we show that our autocorrelation matrix exponential random variables produce more accurate performance metrics from simulation models than traditional techniques.

Teaching elementary queueing theory with a computer algebra system

Computer algebra systems such as Maple, Mathematica and MACSYMA are readily available for a wide range of PCs and workstations. Many college campuses have site licenses for these software tools and make them widely available to students through PC labs, across networks and on time sharing systems. Additionally student versions of these software tools are widely available at nominal cost. Computer algebra systems provide sophisticated computational support and are intuitive to use. In this paper we describe how we use a computer algebra system to support an upper division undergraduate course teaching elementary queueing theory. We discuss the significant enhancement added by using a computer algebra system for this course work. We present the traditional approach to this material, i.e., deriving the closed form solutions for a specific queueing model then we show how we approach the material using numerical solutions based on the general equations for steady state probabilities for a Poisson Birth-Death process. We present several examples and discuss the strengths of our approach.

FCFS: a novel scheduling policy for tightly-coupled parallel computer systems

Tightly-coupled parallel computer systems are available from several vendors. The mechanism for process scheduling employed by virtually all of these systems is preemptive by job priority. This scheme for process scheduling consumes significant processor resources and can result in significant processor contention for the scheduling data structure. In this paper we show that it is possible to reduce the number of job priorities, and at the same time reduce the administrative overhead on the system, without significantly increasing job wait time. Also we show, by four simulation studies, that non-preemptive scheduling mechanisms are just as effective as preemptive techniques when coupled with time slice control and multiprogramming limits. Thus simplified scheduling techniques that require little overhead to prevent processor contention may be employed in a tightly coupled parallel environment without sacrificing either mean response time or the &sgr; of response time.

An analytic model of the leaky bucket with general distributions for both token and cell arrivals

Abstract In this paper we present a linear algebra queuing theory implementation of the leaky bucket traffic shaping mechanism. We develop explicit equations for steady-state and transient behavior. We also derive inter-departure times for the leaky bucket cell departure stream, compute its moments and study its transient behavior. We show that the linear algebra queuing theory approach to modelling the leaky bucket provides a clear and concise technique for analyzing its behavior. We present several examples of the linear algebra queuing theory approach to modelling the leaky bucket with various cell arrival and token arrival distributions.

An algorithm based on queue migration for mutual exclusion in computer networks

A non-symmetric algorithm is presented that achieves mutual exclusion in a decentralized computer network by exchanging messages and a synchronization queue. The algorithm is unique in the sense that the number of messages required to achieve mutual exclusion is a function of the workload enabling it to provide acceptable performance in a lightly loaded system with a significant improvement as the workload increases. The algorithm outperforms other previously proposed algorithms in a heavily loaded system, is robust and comparatively easy to implement.

Evaluating Police Department Policy Decisions Using a Simulation Model of Sworn Officer Deployment

In this paper we describe a simulation model built to study police manpower planning and scheduling at the strategic level. The model was designed to analyse current officer shift scheduling and to report average response time for different classes of calls and utilisation of patrol officers. Since the model produces officer utilisation, it could be used as a planning tool supporting shift scheduling, budgeting for new officers and supporting community policing efforts. We describe construction, verification and validation and the parameters for the model. We present results from a baseline study and we show how our model could be used to support several policy decisions about officer utilisation and deployment.