Customer Flow Research Articles

Flow Time in theMAP/G/1Queue with Customer Batching and Setup Times

This paper studies flow times in a single server queue with customer batching and setup times. Customers arrive according to a Markov arrival process where every N consecutive customers are gathered into a batch before service. The service time of a batch consists of a setup time followed by N individual processing times. The customer flow time, an important measure in production management, is defined as the time between the arrival of an arbitrary customer and the time its batch leaves the system. The main result of this paper is the Laplace Stieltjes transform of the customer flow time, from which the mean and variance of the customer flow time are derived. An extension of existing results for the MAP/G/1 queue is used to develop an algorithm for computing the mean and an approximation to the variance of the customer flow time. The relationship between the burstiness of the input process and the mean flow time, flow time variance and the corresponding optimal batch sizes is explored with numerical examples

Is it time for computer-assisted decision making to improve the quality of food and nutrition services?

Is it time for computer-assisted decision making to improve the quality of food and nutrition services?

A QUEUEING ANALYSIS OF PRIORITY-BASED SCHEDULING RULES FOR A SINGLE-STAGE MANUFACTURING SYSTEM WITH REPAIR

Abstract In many manufacturing settings, an item may require repair at one stage before it is passed on to the next manufacturing operation. This paper examines a single-stage manufacturing system in which all items require a processing operation, they are then inspected, and a fraction (1-p) require rework. Two priority-based scheduling rules, motivated by the goal of minimizing the mean flow time in the repair system, are considered- The LST of the flow time PDF for a random arrival is developed for each priority rule. From the LST, the mean and variance of customer flow times can be obtained. Computational experience with the two rules is reported along with a discussion of the preferability of each rule when both flow time mean and variance are considered as performance measures.

G-networks by triggered customer movement

The generalized queueing networks (G-networks) which we introduce in this paper contain customers and signals. Both customers and signals can be exogenous, or can be obtained by a Markovian movement of a customer from one queue to another after service transforming itself into a signal or remaining a customer. A signal entering a queue forces a customer to move instantaneously to another queue according to a Markovian routing rule, or to leave the network, while customers request service. This synchronised or triggered motion is useful in representing the effect of tokens in Petri nets, in modelling systems in which customers and work can be instantaneously moved from one queue to the other upon certain events, and also for certain behaviours encountered in parallel computer system modelling. We show that this new class of network has product-form stationary solution, and establish the non-linear customer flow equations which govern it. Network stability is discussed in this new context.

G-networks by triggered customer movement

The generalized queueing networks (G-networks) which we introduce in this paper contain customers and signals. Both customers and signals can be exogenous, or can be obtained by a Markovian movement of a customer from one queue to another after service transforming itself into a signal or remaining a customer. A signal entering a queue forces a customer to move instantaneously to another queue according to a Markovian routing rule, or to leave the network, while customers request service. This synchronised or triggered motion is useful in representing the effect of tokens in Petri nets, in modelling systems in which customers and work can be instantaneously moved from one queue to the other upon certain events, and also for certain behaviours encountered in parallel computer system modelling. We show that this new class of network has product-form stationary solution, and establish the non-linear customer flow equations which govern it. Network stability is discussed in this new context.

G-Networks with Signals and Batch Removal

We consider queueing networks containing customers and signals that were recently introduced in Gelenbe [4]. Both customers and signals can be exogenous or can be obtained by a Markovian transition of a customer after service. A signal entering a queue forces a customer to move on to another queue according to a Markovian routing rule or to leave the network in batch mode. This synchronized or triggered motion is useful in representing the effect of tokens in Petri-nets, for systems in which customers and work can be instantaneously moved from one queue to the other on the arrival of a signal as well as for other network behaviors that are encountered in parallel computer system modelling. We show that this network has product form stationary solution and establish the non-linear customer flow equations that govern it. Network stability is discussed in this new context.

Optimal Location of Discretionary Service Facilities

Automatic teller machines and gasoline service stations are two examples of a growing number of “discretionary service facilities.” In consuming service from these facilities, a significant fraction of customers do so on an otherwise preplanned trip (e.g., on the daily commute to and from work). A system planner, in determining the best locations of such facilities, is more concerned with placing the facilities along paths of customer flow rather than, say, near the center of a cluster of residences or work places. We formally model this problem and present a method for determining the optimal locations of m discretionary service facilities so as to intercept the maximum possible potential customer flow. We also show how to determine the minimal number of facilities required to intercept a prespecified fraction of total customer flow. Computational results are included.

Stability of Product Form G-Networks

We prove necessary and sufficient conditions for the existence and uniqueness of the stationary solution of the queueing networks (G-networks) with negative and positive customers introduced in Gelenbe [3], which have been shown to have product form. First, the existence of the solution of the nonlinear customer flow equations is established using Brouwer's fixed-point theorem; this result is valid for stable and unstable systems, as well as for certain networks that may not have product form. Then, the result is used to establish general stability related to the usual “load factor less than 1” criterion of queueing systems for G-networks with product form.

THE TWO WAYS IN WHICH RETAILERS CAN BE BRANDS

Retailers, it is said, are behaving as brands. Tests whether retailers can be considered to be brands by comparing the current practices of British retailers against four criteria for a brand which are developed from the existing literature on branding. The four criteria are that the brand should: differentiate; be capable of a separate existence; command a premium price and; offer the customer some psychic value. Concludes that retail brands not only exist but also exist in two forms: the more obvious merchandise brands, commonly known as own‐brand that are now marketed as more than generic commodities; and the less obvious process brand that represents the experience that retailers provide. Argues that the process brand is purchased with the shoppers′ time rather than with their money. The process brand has value to the retailer as it generates customer flow, customer loyalty and higher expenditure.

Product-form queueing networks with negative and positive customers

We introduce a new class of queueing networks in which customers are either ‘negative' or ‘positive'. A negative customer arriving to a queue reduces the total customer count in that queue by 1 if the queue length is positive; it has no effect at all if the queue length is empty. Negative customers do not receive service. Customers leaving a queue for another one can either become negative or remain positive. Positive customers behave as ordinary queueing network customers and receive service. We show that this model with exponential service times, Poisson external arrivals, with the usual independence assumptions for service times, and Markovian customer movements between queues, has product form. It is quasi-reversible in the usual sense, but not in a broader sense which includes all destructions of customers in the set of departures. The existence and uniqueness of the solutions to the (nonlinear) customer flow equations, and hence of the product form solution, is discussed.

Product-form queueing networks with negative and positive customers

We introduce a new class of queueing networks in which customers are either ‘negative' or ‘positive'. A negative customer arriving to a queue reduces the total customer count in that queue by 1 if the queue length is positive; it has no effect at all if the queue length is empty. Negative customers do not receive service. Customers leaving a queue for another one can either become negative or remain positive. Positive customers behave as ordinary queueing network customers and receive service. We show that this model with exponential service times, Poisson external arrivals, with the usual independence assumptions for service times, and Markovian customer movements between queues, has product form. It is quasi-reversible in the usual sense, but not in a broader sense which includes all destructions of customers in the set of departures. The existence and uniqueness of the solutions to the (nonlinear) customer flow equations, and hence of the product form solution, is discussed.

Practical management of a shopping centre

The most important factor in generating customer flow in a shopping centre lies in the quality of its tenant mix.

Queues with delayed feedback

Queues with delayed feedback have been little studied in queueing theory. Presented here is a rather complete discussion of such problems including queue length processes, busy period processes and several customer flow processes (e.g., departure processes). The case in which the delay mechanism is an M-server queue is studied in detail but it is shown later that many of the results carry over to a more general delay mechanism.

Queues with delayed feedback

Queues with delayed feedback have been little studied in queueing theory. Presented here is a rather complete discussion of such problems including queue length processes, busy period processes and several customer flow processes (e.g., departure processes). The case in which the delay mechanism is an M-server queue is studied in detail but it is shown later that many of the results carry over to a more general delay mechanism.

待ち行列問題の連続モデルを利用する近似解法II : 複数窓口有限待ち行列

An approximation method based on the diffusion theory is proposed for solving multi-server finite queueing problems having general independent inter-arrival time and general service time distributions. The discrete customer flow through the system is approximated by a continuous one, and a diffusion equation for the process of the number of customers in the system is constructed by using means and variances of the inter-arrival time and service time distributions. Two reflecting boundaries are imposed at the origin and m, the maximum number of customers being allowed in the system. Later, the boundary conditions are modified to improve the approximation. Approximate formulas for P_n. Probability of finding n customers in the system, and for N, mean number of lost customers from the system per mean service time, are given for steady state. Numerical examples for mean number of customers in the system are presented for some E_l/E_k/s(m) systems to show the effectiveness of the proposed method.

Improving the flow of customers in a hospital cafeteria

Customer flow through a hospital cafeteria was modeled as a queuing system for the purpose of analyzing the problems of long lines and excessive waiting by customers during lunch hours. Different policies of the hospital affecting the arrival times of customers to the cafeteria were simulated on a computer. The key factor was found to be group arrivals because of the pattern in which the hospital departments released their employees for lunch. Alternative policies were simulated, and performance with those policies in effect was measured and reported.

Matching staff levels to customer flow

Simply reducing numbers is not the most effective way of cutting staff costs; the secret is to match staff levels with anticipated customer flow. It not only saves money, but it gives better service to customers. Bob Forrester describes how the application of this system in a department store on Merseyside achieved staff costs as a percentage of sales 2.63% below the group figure, whilst the sales increase was the second best in the group.