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...to customers fairly accurate information about anticipated delays due to congestion. Such information can directly affect customer satisfaction and also influence customers' behavior. Here, we focus on the arriving customer's decision to wait for service or to leave (balk).
For example, in a call center, the provider can announce the expected waiting time to each caller; standard call-center software can do this automatically. In transportation and e-shopping, a customer can easily learn the order status and the estimated shipping time. A quote for production services normally includes a lead-time estimate. In a busy hospital emergency room, information about the anticipated wait is important to an anxious patient. Delay notification is used in traffic-flow control; in some cities, congestion conditions are shown on big electronic boards at highway entrances. A similar idea has been suggested for control of computer networks; see, e.g., Kelly (2000).
Information can take many forms, with different degrees of precision. Different levels of information have different effects on customers' decisions and thus the overall arrival process. The goal of this paper is to develop and analyze models to explore these effects. We consider three typical types of delay information: none, the system occupancy, and the exact waiting time. With no information, customers still estimate their waiting times, but these estimates are based only on long-term (equilibrium) experience, not real-time information. The occupancy provides partial information; the remaining uncertainty comprises the actual service times of the waiting customers. The exact waiting time gives the customer full information. We assume that the information provided is truthful, and customers believe it.
Depending on the situation, it can be hard or easy, expensive or cheap, for the provider to obtain delay information and transmit it to customers. Some amusement parks post signs in waiting areas indicating expected delays based on distance to the head of the line. That information is cheap. In other settings, information requires a substantial investment in technology. Here, we do not discuss such costs, but rather focus on the benefits.
We assume Poisson arrivals and independent, exponential service times. There is a single server using the first-come-first-served (FCFS) discipline.
To assess the effects of information consistently, we posit a customer-decision mechanism common to all levels of information. A given function measures the basic cost of delay. Different customers, however, value time differently. Each customer arrives with a specific parameter, which scales the basic cost function. Upon arrival the customer receives information, which affects his estimate of the distribution of delay. Based on his scale parameter and the information, the customer computes his expected delay cost. If that is more than the reward he anticipates from receiving service, he balks, and if not, he stays. In this scheme, then, different levels of information lead to different delay distributions in the expected-cost calculations, and those in turn affect everything else. We assume that the service provider cares about the throughput, perhaps because he receives a payment for each customer served.
We show how to compute the key performance characteristics for each of the three information scenarios. Then, we compare the results to assess the impacts of information. These impacts turn out to be subtle. One might expect more information always to be better, but it is not. The effect depends mainly on the form of the cost-scale parameter distribution.
An overview of customer psychology in waiting situations, including the impact of uncertainty, can be found in Maister (1985). There is some empirical evidence about customers' reactions to delays. Taylor (1994) shows that delays affect customers' overall service evaluations. Hui and Tse (1996) and Kumar et al. (1997) study the relationship between information and customer satisfaction. Munichor and Rafaeli (2007) examine the impact on customers' waiting-time perceptions of the use of various waiting-time fillers. Zhou and Soman (2003) examine the determinants of reneging behavior.
There is a substantial literature on queues with impatient customers. Models with balking and reneging (leaving after waiting for some time) can be found in many books, e.g., Kulkarni (1995). Recent works on this topic include Bae et al. (2001), Zohar et al. (2002), and Ward and Glynn (2003).
The literature on customers influenced by delay information begins with Naor (1969), who studies a system like ours with partial information, but with identical customers and linear waiting cost. Also, the cost depends on the whole sojourn time, not just the delay. He points out that this system with its self-selecting customers suffers from externalities; an arriving customer who stays imposes delays on later customers, but ignores them in making his decision. Consequently, too many customers stay. If everyone were altruistic and acted to maximize the average utility, some of those customers would leave. He shows that a price can steer the system to this "social" optimum. He points out, however, that if the price is determined by the provider to maximize revenue, the provider becomes a monopolist and behaves like one. He sets the price higher than the socially optimal one and thus serves too few customers.
These features lead to additional peculiarities. Edelson and Hildebrand (1975) mention that a revenue-maximizing service provider may make socially wrong decisions about service capacity, either in the service rate or the number of servers. They also show that these effects disappear when balking...
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