ABSTRACT
The problems of organization to meet the rising tide of traffic congestion, patron complaint and increased costs appear, for some time now, to characterize the operation of vehicular toll collection at the Lagos - Ibadan expressway toll booth. It is the principal purpose of this research to study the weekend peak traffic delays at this facility by analyzing the queueing problem. This issue is addressed here in order to evaluate the level of service given to patrons and to seek a better understanding of the factors contributing to the poor toll booth service and the means by which service could be improved. Two policemen constitute a set of parallel servers and vehicles leave them for the toll collectors who constitute another set of six parallel servers. Thus a tandem queueing situation, in which capacity restrictions are imposed, is identified for the system. Specifically, it is a truncated 2-stage serial queue. It has two parallel servers at the first stage and six parallel servers at the second stage. Vehicles are of different types and the servers are different from one another while order of service is first come first served. Data is collected and analyzed using explanatory and confirmatory statistical techniques in order to suggest possible theoretical models that can persimoniously describe the behaviour of the variables of interest for the system. In particular the possibility of a poisson arrival and an exponential service time for all channels at both stages is fully explored and the possibility for stationary ineuts and aggregation of data is surveyed through statistical methods. A one-way analysis of variance and curve fitting using the Kolmogorov-Smimov (K-S) test, are carried out on sets of the data and the poisson/exponential assumptions are fairly justified. A computer programme is written for use with the curve fitting technique. An approximate low fidelity analytical model with the general capability of predicting the 'steady state' performance of the toll booths under a wide range of different physical and operational condition Is then sought to provide operational solutions to the problem. A survey of candidate models from existing queueing literature suggests an appropriate base model which is modified and adopted for this study. The expected waiting time, mean number in line (excluding the first queue), the customer loss ratio and all other measures of system effectiveness which are of operational interest are then obtained from the model equations using a computer programme designed to evaluate these performance measures. These system effectiveness measures constitute the basic model output and to validate this analytic/predictive model some of these predicted measures are compared with those measured under same conditions of input. Finally, a few numerical results are tabulated and a graphical illustration shown. Recommendations are then made on how to improve operations and the thesis concludes by touching upon questions yet unsolved.