A new procedure to estimate waiting time in GI/G/2 system by server observation

Abstract Most GI/G/2 queueing formulae need the variance of inter-arrival time, which is in many cases more difficult to estimate than the other values used in the formulae such as the mean of inter-arrival time, mean of service time and variance of service time. This paper presents a new GI/G/2 queueing formula which uses a slightly different set of data easier to obtain than the variance of inter-arrival time. The key variables are the numbers of system busy periods and system idle periods. Also, it is shown, by simulation, that the waiting time estimation error from the new formula is far less than other popular queueing formulae which use the first two moments of service time and inter-arrival time over a wide range of coefficient of variation. Scope and purpose Waiting is very common in our daily life, and the estimation is sometimes very important for the design of service and manufacturing systems. If the number of barbers at a barber's shop is too small, customers frequently wait for the service too long. If the number of machines in a manufacturing shop is too small, the production lead time from order entry to product delivery can be very long. The waiting time is closely related not only to the average service requirement but also to the variability of it. If customers require service at the same time, the average waiting time of the customers will be longer than the average waiting time with even requests. Traditionally, the variance of inter-arrival time has been used to represent the variability; however, estimation of the variance needs observation of customer arrivals, which often needs much effort. This paper presents another procedure to estimate the waiting time. This procedure does not need the observation of customers. The estimation of waiting time for bank teller machines can be a good application example of this new procedure because the machines do not have the arrival data of the customers. The procedure presented here is for a two parallel server case.