Customers In Queue Research Articles

Monopoly pricing when customers queue

It takes time to process purchases and as a result a queue of customers may form. The pricing and capacity (service rate) decision of a monopolist who must take this into account are characterized. We find that an increase in the average number of customers arriving in the market either has no effect on the price, or else causes the firm to reduce the price in the short run. In the long run the firm will increase capacity and raise the price. When customer preferences are linear, the equilibrium is socially efficient. When preferences are not linear, the equilibrium will not normally be socially efficient.

Mode Locking and Chaos in a Deterministic Queueing Model with Feedback

We consider a simple, deterministic queueing system with feedback, which exhibits the phenomena of sustained oscillation, mode locking, quasi-periodic behaviour, and chaos. This implies that a fully deterministic queueing system can exhibit seemingly unpredictable behaviour. We ignore variability, and focus on two forms of feedback: (i) the service rate increases as queue length increases, and (ii) the arrival rate depends on customers' perception of past waiting times. We model a customer's decision to seek service as a two stage process: (i) deciding whether or not to use a facility, and (ii) deciding the frequency of visit (daily, weekly, monthly, etc.). This frequency is initially constant, and later on replaced by a deterministic, time-dependent pattern. Although highly stylised, this model captures the essential features of many real-life systems whose average arrival rate varies over time. Reducing the amplitude of cycles in demand makes the system more predictable and thus easier to manage. Although we represent this model as a queue of customers waiting for service, the model can be interpreted more generally as any situation where an increase in demand lowers the quality of service.

A queueing control model for retail services having back room operations and cross-trained workers

Many retail service facilities have both front room and back room operations. The front room deals with serving customers, perhaps from a queue. The back room focuses typically on restocking of shelves and sorting and/or processing of paperwork. We model such a facility having workers who are cross-trained to do both jobs. We assume that back room work is interruptible. A manager can bring a worker from the back room to the front room when the customer checkout queue becomes “too long”. A reverse assignment occurs when the number of customers is sufficiently small. We assume that the retail facility contains two customer-counting technologies. The first counts the number of shoppers in the store who are not already in checkout queues and the second counts the number of customers at checkout. The goal is to find the minimum number of workers to staff the facility subject to two performance constraints. The mean queue delay in the front room must be less than a pre-specified value, and the time-average number of workers in the back room must be greater than a pre-specified value. Once the minimum complement of workers is found, a secondary goal is to minimize mean queueing delay subject to retaining back room feasibility. The system is a continuous time Markov process having a three-dimensional state space. The (heuristic) optimization process includes state-dependent rules for switching workers between rooms. Scope and purpose Many customer service facilities have both front room and back room operations for workers. In the front room, workers serve customers who may be delayed in a queue. In the back room workers perform required but time-insensitive work such as restocking of shelves, sorting of materials and/or processing of paperwork. Allowing workers to be cross-trained to perform both functions creates a potentially high productivity system with worker utilization rates near 100%. We model such a facility having workers who are cross-trained using techniques of queueing theory and heuristic optimization. The assignment of workers over time to each of the two tasks is dependent on the number of customers in the front room. When the customer queue becomes “too long”, the manager can bring a worker from the back room to front room and vice versa when there are few customers in the front room. The goal is to find the minimum number of workers to staff the facility subject to performance constraints in both rooms: a mean queue delay constraint in the front room and an average number of workers constraint in the back room. Of particular interest is determining the rules for bringing in and sending back workers.

Admission control and scheduling in simple series parallel networks using fuzzy logic

Two outstanding problems of admission control and scheduling in networks with three and two workstations, respectively, are solved using fuzzy logic. Neither problem has been tackled up until now analytically, whereas the fuzzy approach provides computational solutions. In the first case, we have one workstation with two parallel ones. A reward is earned whenever the first stage accepts a customer and a holding cost is incurred by a customer in queue in the second stage. The class of customer to be next served by the first stage is dynamically selected so as to maximize an average benefit over an infinite horizon. In the second case, there are two parallel servers and three arrival processes generated by independent Poisson streams. Each server has its own queue and receives customers from its own arrival stream. A third arrival stream consists of customers with resource demand on both servers. Each customer pays a holding cost per unit time in the system. Again, the scheduling policy is specified which minimizes the average cost. The fuzzy models are new in this context and tackle computationally problems for which we have not analytical solutions.

Some well-behaved estimators for the M/M/1 queue

It is known that, given the observed traffic intensity ρ <1 , the expected value of the estimator ρ /(1− ρ ) for the average number of customers ρ/(1− ρ) in a stationary M/M/1 queueing model is infinite (Schruben and Kulkarni, Oper. Res. Lett. 1 (1982) 75–78). In this paper we generalize the above findings to other system performance measures. Second, we show that, for the following four system performance measures: (a) mean waiting time in queue, (b) mean waiting time in system, (c) mean number of customers in queue and (d) mean number of customers in the system, estimators constructed by substituting parameter estimators for unknown parameters in the formula for the performance measure all have the undesirable properties that the expected value of the estimator does not exist and the estimator has infinite mean-squared error. Finally, we propose alternative estimators for these four system performance measures when ρ< ρ 0, where ρ 0<1 is a known constant, and show that these alternative estimators are strongly consistent, asymptotically unbiased and have finite variance and finite mean squared error.

Using simulations in the optimisation of fast food service delivery

This research focuses on the UK fast food retailers and the importance of the service delivery systems in fast food burger outlets. Waiting time and the impact it has on customer perceptions of service quality is considered alongside a typology of customers, based on their waiting characteristics. A number of critical components that affect customer queuing and crowding emerge as an inherent part of the production‐line service system. The paper asserts that the cost‐effective maximisation of service speed is likely to be the primary consideration for management, and lead to business success. When using conventional research approaches, such as tracking studies and queuing theory, these arguably offer burger restaurant managers a rather simplistic analysis. The research concludes, therefore, that modern computer‐based simulation packages offer a way of measuring most of the influencing factors, and is an opportunity for leading fast food retailers to optimise their (total) product positioning.

Service-methods and management

Service-methods and management

Simultaneous Service Approach for Reducing Air Passenger Queue Time

Simultaneous service offers service-oriented organizations, such as the air passenger transportation industry, the opportunity to differentiate themselves by providing superior customer service. The concept of simultaneous service is analogous to the concept of simultaneous engineering. However, while simultaneous engineering strives to minimize product development time, simultaneous service strives to minimize customer processing time. Overall customer processing time is reduced by the identification and simultaneous alignment of previously sequentially executed customer service activities. A simultaneous service approach was applied to the international ticketing counter at a major international airport. This involved developing both equipment and operational policy alternatives to the normal sequencing of the ticketing and baggage check-in process. A total of five alternative simultaneous service approaches were investigated. Simulation analysis of these alternatives indicates that a 36% improvement in customer queue and servicing time was possible with this approach.

Fuzzy assignment of customers for a queueing network

This paper considers a queueing network with two parallel heterogeneous servers. Each server has its own queue and customers arrive at each queue according to independent Poisson processes. Service times are independent and exponentially distributed. When a customer arrives at queue 1, the customer can be transferred to queue 2 by paying an assignment cost. Each customer in queue pays a holding cost per unit time. The objective is to dynamically determine the optimal assignment policy so as to minimize the average cost. In this paper, a novel approach is presented using fuzzy control to solve the problem.

The Impact of Waiting Time Guarantees on Customers' Waiting Experiences

Customers often have to wait during the process of acquiring and consuming many products and services. These waiting experiences are typically negative and have been known to affect customers' overall satisfaction with the product or service. To better manage these waiting experiences, many firms have instituted a variety of programs not only to reduce the actual duration of the wait but also to improve customers' perceptions of it. In this paper, we examine the impact of one such initiative, namely, the institution of a waiting time guarantee, on customers' waiting experiences. A waiting time guarantee is a commitment from a firm to serve its customers within a specified period of time. If the firm fails to meet this commitment for some customers then it compensates them for the delay. Today, a large number of firms in a variety of industries such as fast food, banking, industrial distribution, and healthcare offer such time guarantees to their customers. We develop a utility theory-based model of customers' satisfaction with waiting in line. The model is based upon the assumption that when a customer joins a queue he or she has some prior beliefs about the distribution of service times at the firm. The customer estimates the likely duration of the waiting time on the basis of these beliefs about the service times and the observed queue length. We further assume that as the customer observes the service times for other customers who are ahead in the queue, he or she successively updates these beliefs about the distribution of service times in a Bayesian manner. We then posit that the customer's satisfaction both during as well as the end of the wait is determined by the difference between the customer's updated and the prior estimates of the total waiting time. We apply the model to derive select hypotheses pertaining to the impact of a waiting time guarantee on customers' waiting experiences. These hypotheses are based upon the assumption that an offer of a time guarantee is a signal of reliability from the firm and reduces customers' perceived variance around the expected service times. We empirically test these hypotheses using data from a series of interactive, computer-based laboratory experiments. In these experiments, we used the computer to create animations of reallife waiting experiences. The computer display consisted of a queue of customers waiting for service at a counter. One of the customers represented the participant in the experiment. During the course of the experiment, each participant joined the queue, waited in line for service, and then exited the system. At several points during the wait, each participant reported his or her level of satisfaction with the waiting experience. Our results suggest that if customers observe the service times to be less than expected, their satisfaction increases monotonically during the wait. Further, under such circumstances, the explicit provision of a waiting time guarantee enhances satisfaction both during as well as at the end of the wait. However, if customers observe the service times to be more than expected, then their satisfaction typically declines at the beginning of the wait but increases toward the end of the wait. Further, under these circumstances, the initial positive impact of the provision of a waiting time guarantee declines over time. Moreover, at the end of the wait, customers in guaranteed environments are actually less satisfied than those in unguaranteed environments. Overall, we find that a time guarantee, if met, increases satisfaction at the end of a wait; however, if violated, then it decreases satisfaction at the end of the wait. We discuss the implications of these and other empirical findings for the management of customers' waiting experiences.

Optimal assignment policy of a single server attended by two queues

A single server attends to two separate queues. Each queue has Poisson arrivals and exponential service. There is a switching cost whenever the server switches from one queue to another. The objective is to minimize the discounted or average holding and switching costs over a finite or an infinite horizon. We show numerically that the optimal assignment policy is characterized by a switching curve. We also show that the optimal policy is monotonic in the following senses: If it is optimal to switch from queue one to queue two, then it is optimal to continue serve queue two whenever the number of customers in queue one or in queue two decreases or increases, respectively.

An assignment problem for a parallel queueing system with two heterogeneous servers

In this paper, we consider an optimization problem for a parallel queueing system with two heterogeneous servers. Each server has its own queue and customers arrive at each queue according to independent Poisson processes. Each service time is independent and exponentially distributed. When a customer arrives at queue 1, the customers in queue 1 can be transferred to queue 2 by paying an assignment cost which is proportional to the number of moved customers. Holding cost is a function of the pair of queue lengths of the two servers. Our objective is to minimize the expected total discounted cost. We use the dynamic programming approach for this problem. Considering the pair of queue lengths as a state space, we show that the optimal policy has a switch over structure under some conditions on the holding cost.

Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian network models. Our main conclusion is that in many respects dynamic routingsimplifies the behaviour of networks, and that under good control policies it may well be possible to model the aggregate behaviour of a network quite straightforwardly.

Productivity Enhancing Customer Delay: Estimates from Physician Data Corrected for Measurement Error

When the physical presence of the consumer is a required part of the production process, firms often adopt a customer queuing mechanism that combines appointment scheduling with an additional delay at point of service. For example, physicians asked the question, On average, how many minutes does a patient typically have to wait to see you after arriving for a scheduled appointment?, reported an average expected DELAY of twenty minutes [2, 92; 3, 78]. DeVany et al. [9] report a nine-minute expected DELAY for dental office visits. This additional DELAY increases the time cost of service to the customer [4, 15, 7] but also reduces scheduling problems caused by variation in provider service and customer arrival rates. Thus, the DELAY queue is posited to increase productivity by reducing the likelihood and length of breaks in the production process. Theoretical models based on the hypothesis that patient delay enhances provider productivity are presented in Sloan and Lorant [21], House [13], DeVany et al. [8; 9], DeVany and Saving [10], McCarthy [15], and Mueller [16]. Empirical evidence, though limited, is with the theoretical hypothesis. It is, however, based on methods that fail to meet one or more of the conditions necessary for parameter estimation when, as is argued in this paper, reported DELAY is stochastic due to measurement error in the available survey data. In spite of this growing body of theoretical literature, DeVany et al. [8] is the only other study that directly tests the hypothesis. Based on Ordinary Least Squares (OLS) regression, their data and marginal product of patient delay estimate of .48 indicate that a five-minute decrease in patient delay would decrease the weekly output of a dental firm by 2.4 visits. Citing Zellner et al. [23], the authors argue that although output and patient delay are jointly determined in their theoretical model because . . the entrepreneurial maximand is stochastic, OLS estimates are unbiased and consistent [8, 151, footnote 11]. This conclusion hinges, however, on the assumption that the patient delay and output error terms are uncorrelated. That assumption easily may be violated by data in which both measures depend on survey respondent recall.

Exchangeable Items in Repair Systems: Delay Times

We compute the delay time distribution for a customer who delivers a failed item to a repair system, when the items are exchangeable and the customer accepts any repaired item that is offered when he is at the head of the customer queue.

A queueing model of finite and infinite source interaction

An M/ M/1 service system is considered, which also serves one finite source. The joint distribution of queue length at the M/ M/1 queue and position of the finite source customer in the system is determined. This leads to exact expressions for various performance measures; such expressions yield insight into the interaction of finite and infinite sources.

Waiting-Time Moments In The Queueing System GI/Ma,b/1

This paper deals with the queueing system GI/Ma,b/1 Expressions are derived for the moments of the steady-state waiting time (in queue) and the moments of the conditional waiting time (in queue) of customers who are mth in their batch. Sample numerical results are presented for the first two moments of the former. The results demonstrate that models of this kind become relatively insensitive to the coefficient of variation of the interarrival-time distribution as the capacity increases. They permit the quantitative assessment of waiting-time costs over a wide range of traffic intensity, quorum, and capacity.

Exponential Queues with Server Vacations

In this paper, we analyse a queueing system where the server may take a vacation. The customers arrive at the service facility according to a Poisson process, and are served if the server is available (not on vacation). We consider two models: when the server vacation cycle is independent of and dependent on the number of customers in the system. The infinitesimal generators of the underlying Markov processes have a block tri-diagonal structure, and we provide a matrix geometric solution. When the vacation cycle is independent of the customer queue length, we present a simple load-dependent approximation that is fairly accurate.

Overload Performance of Several Processor Queueing Disciplines for the M/M/1 Queue

In a Variety of overloaded queueing systems (e.g., an overloaded call processing system), long delays can result either in poor service given to the customer or in customers, unknown to the system, turning bad. For example, in switching systems, long dial tone delays can result in customers initiating dialing before receiving dial tone. In this case the system will not receive all the digits and an unsuccessful call results. This can lead to the system expending real time on unsuccessful services and, therefore, reduces the effective throughput. Thus, there is a need for control Schemes which reduce the load offered to the processor by selectively refusing service to some customers in such a way as to keep delays, for those customers which are selected for service, small. This fact has been recognized and has led to improved strategies for local switches. In this paper we analyze and compare the performance of various queueing and service disciplines for an M/M/1 queue. We consider LIFO and FIFO Schemes with customer rejection mechanisms corresponding to pushing out or timing out older customers in queue. Delay distributions for served customers are obtained and comparisons based upon throughput-delay tradeoffs are presented. For the situation where Customers can turn bad at a random time after their arrival, we compare the throughput of good customers. The results presented are a mixture of classical results, which are briefly stated, and new results which are developed in more detail. The numerical results show a dramatic effect of the queueing and Service disciplines on the overload performance and a strong dependence of the throughput of successful services on the mechanism for customers turning bad. Although results are obtained for a single server queue, they can be used to approximately analyze overload control schemes which control access to distributed systems.

An M/G/c queue in which the number of servers required is random

Many queueing situations such as computer, communications and emergency systems have the feature that customers may require service from several servers at the same time. They may thus be delayed until the required number of servers is available and servers may be idle when customers are waiting. We consider general server-completion-time distributions and derive approximation methods for the computation of the steady-state distribution of the number of customers in queue as well as the moments of the waiting-time distribution. Extensive computational results are reported.