Moments Of Service Times Research Articles

The impact of order batching and picking area zoning on order picking system performance

This paper proposes an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. The model includes the sorting process needed to sort the batch again by order. Service times at pick zones are assumed to follow general distributions. The first and second moments of service times at zones and the visiting probability of a batch of orders to a pick zone are derived. Based on this information, the mean throughput time of an arbitrary order in the order picking system is obtained. Results from a real application and simulation show that this approximation model provides acceptable accuracy for practical purposes. Furthermore, the proposed method is simple and fast and can be easily applied in the design and selection process of order picking systems.

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

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.

Characterization of the Stochastic Median Queue Trajectory in a Plane with Generalized Distances

We characterize the trajectory of the Stochastic Queue Median (SQM) location problem in a planar region with discrete demands and a general Lp travel metric (1 < p < ∞). The location objective is to minimize expected response time to customers (i.e., travel time plus queue delay). We use an ε-perturbed version of the SQM objective function (to account for points of nondifferentiability) to show that for the ε-perturbed problem the optimal SQM location occurs in a region bounded by the point minimizing the first and second moments of service time (s*∣ε and s2*∣ε, respectively); all optimal locations can be characterized by a simple ratio condition relating the derivatives of the first and second moments of service time; and the trajectory as a function of the customer call rate moves monotonically along a path from s*∣ε toward s2*∣ε, then turns and retraces the same path back to s*∣ε. Finally, we establish convergence of the ε-optimal solution to an optimal SQM solution as ε approaches zero, as well as a general condition under which we can solve the SQM problem directly, with no perturbation.