Development of a Heuristics Model for Simplifying a Multi-Channel Queuing System

摘要

Queuing model has been discussed widely in literature. The structures of queuing systems are broadly divided into three namely; single, multi-channel, and mixed. Equations for solving these queuing problems vary in complexity. The most complex of them is the multi-channel queuing problem. A heuristically simplified equation based on relative comparison, using proportionality principle, of the measured effectiveness from the single and multi-channel models seems promising in solving this complex problem. In this study, six different queuing models were used from which five of them are single-channel systems while the balance is multi-channel. Equations for solving these models were identified based on their properties. Queuing models' performance parameters were measured using relative proportionality principle from which complexity of multi-channel system was transformed to a simple linear relation of the form A =αA'. This showed that the performance A obtained from single channel model has a linear relationship with A' corresponding to multi-channel, and α is a factor which varies with the structure of queuing system. The model was tested with practical data collected on the arrival and departure of customers from a cocoa processing factory. The performances obtained based on average number of customers on line n_l, average number of customers in the system n_s, average waiting time in line t_l and average waiting time in the system, t_s under certain conditions showed no significant difference between using heuristics and analytical models.