Modelling waiting time in queues

Abstract

The Mathematical study of queue waiting time is mainly concerned with queue performance measures where several applications have been drawn in past studies. Among the vast uses and applications of the theory are the various queues experienced in day to day lives where the theory has been used to solve the problem of long queues which leads to resource waste. In recent developments, the electronic quality management systems have been adopted to manage queues which can be used in assessment, analysis and even more consequentially to estimate the average queuing times in waiting lines as well as to reveal the steady state properties of queues. Ultimately, these queue performance measures are used to make decisions on improving services. Single server stochastic queuing models have been studied and used extensively to model the mean waiting time in queues. There is need to utilize a joint model comprising of both stochastic and deterministic queuing models in order to solve the inadequacies of the non-randomness property of the stochastic models. This study is intended to model waiting time in queues by use of stochastic and deterministic queuing systems where the main aim of this study was to model waiting time in queues where specifically, models for estimating the mean waiting time were obtained. Consequently, real time queue data was applied on these models and finally, validation of the model through simulation was also performed. To accomplish these, the waiting time in queues was modeled on the basis of both stochastic model represented as M/M/C denoting Markovian arrivals, Markovian service times and multiple (C) servers and a deterministic model represented as D/D/1 denoting Deterministic arrivals, Deterministic service times and one (1) service channel (server). Bank queue data was applied on the models obtained to ascertain whether the various queue performance measures explain the behavior of a queue and to validate the models simulation was performed using MATLAB software. The results reveal that both deterministic and the stochastic delay components are compatible in modeling waiting time. The models also are applicable to real time bank queue data where upon simulation, both models depict a fairly equal waiting times for server utilization factors below 1.For instance when p<1, and an infinitely increasing delay at p>1 In conclusion, the models need to be implemented in queue systems so that queues are more efficient in terms of service delivery.