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

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 = alpha A'. This showed that the performance A obtained from single channel model has a linear relationship with A' corresponding to multi-channel, and alpha 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.