Customers waiting to get service from server are represented by queue and called waiting line. Unsatisfied customer due to long waiting time can be a potential loss to any service organization. Managing waiting lines is one of the foremost objective for service operations manager as prompt service delivery is one of the parameter to achieve competitive advantage.
In this essay we would discuss how analytical models of waiting lines can help managers evaluate the cost and effectiveness of service systems.
We begin with a look at what is a waiting line system and then describe the elements of waiting lines and waiting line performance measures. We also provide and the example to illustrate for these measures.
What Is a Waiting Line System? Queuing theory is also known as the study of waiting lines. This is one of the most used as well as the eldest quantitative analysis techniques known to man (Render, Stair, & Hanna, 2012). Every day and everywhere we go people have to experience waiting lines, whether it’s at the bank making a deposit, students at school at lunch time, shopping at the grocery store, or even on the telephone waiting for the first customer service worker to answer to pay a bill.
The amount of time a person waits in a line is contingent on a few things; how many items you have to buy, how many people are in front of you, in addition to the amount of customer service workers, or cashiers and how fast or well they can perform their jobs.
There are three vital components of a queuing process, and they are when you arrive, the service facilities, and the waiting line (Render, Stair, & Hanna, 2012).
Any time there is more customer demand for a service than can be provided, a waiting line occurs. Customers can be either humans or inanimate objects. Examples of objects that must wait in lines include a machine waiting for repair, a customer order waiting to be processed, subassemblies
In a manufacturing plant (that is, work-in process inventory), electronic messages on the Internet, and ships or railcars waiting for unloading. In a waiting line system, managers must decide what level of service to offer. A low level of service may be inexpensive, at least in the short run, but may incur high costs of customer dissatisfaction, such as lost future business and actual processing costs of complaints. A high level of service will cost more to provide and will result in lower dissatisfaction costs. Because of this trade-off, management must consider what is the optimal level of service to provide.
For example, fast-food restaurants illustrate the transient nature of waiting line systems. Waiting lines occur at a fast-food restaurant drive through during peak meal times each day. There is a temporary surge in demand that cannot be quickly handled with the available capacity. To speed up delivery, some restaurants use an extra window—the first window for paying and the second window for picking up the food. At other times of the day, the restaurant uses a single window and may have no waiting line at the drive-through window.
The challenge is designing service systems with adequate but not excessive amounts of capacity. A fast-food restaurant experiences variable demand and variable service times. The restaurant cannot be sure how much customer demand there will be, and it does not know exactly what each customer will order – each order can be unique and require a different service time. It is important to understand the different elements of a waiting line system. These elements include the customer population source, queue discipline, the arrival and service patterns, and the priorities used for controlling the line.
The customer population can be finite or infinite. When potential new customers for the waiting line system are affected by the number of customers already in the system, the customer population is finite.
When the number of customers waiting in line does not significantly affect the rate at which the population generates new customers, the customer population is considered infinite.
In addition to waiting, a customer has other possible actions. For example, a customer may balk, renege, or jockey. Balking occurs when the customer decides not to enter the waiting line. Jockeying occurs when a customer changes from one line to another, hoping to reduce the waiting time. A good example of this is picking a line at the grocery store and changing to another line in the hope of being served quicker.
The models used in this supplement assume that customers are patient; they do not balk, renege, or jockey; and the customers come from an infinite population. The mathematical formulas become more complex for systems in which customer population must be considered finite and when customers balk, renege, or jockey.
The queue discipline is the order in which waiting customers are served. The most common type of queue discipline is first come, first served–the first person or item in line waiting is served first. Other disciplines are possible. For example, a machine operator might stack in-process parts beside a machine so that the last part is on top of the stack and will be selected first. This queue discipline is last in, first out. Often customers are scheduled for service according to a predetermined appointment, such as patients at a dentist’s office or diners at a restaurant where reservations are required. These customers are taken according to a prearranged schedule regardless of when they arrive at the facility. Queues can be of an infinite or finite size or length. An infinite queue can be of any size with no upper limit and is the most common queue structure.
Waiting line models require an arrival rate and a service rate. The arrival rate specifies the average number of customers per time period. It is the variability in arrival and service patterns that causes waiting lines. Lines form when several customers request service at approximately the same time. This surge of customers temporarily overloads the service system and a line develops. Waiting line models that assess the performance of service systems usually assume that customers arrive according to a Poisson probability distribution, and service times are described by an exponential distribution. The Poisson distribution specifies the probability that a certain number of customers will arrive in each time period (such as per hour). The exponential distribution describes the service times as the probability that a particular service time will be less than or equal to a given amount of time.
The easiest waiting line model involves a single-server, single-line, single-phase system. The following assumptions are made when we model this environment:
Note: The service rate must be greater than the arrival rate, that is Λ; Μ. If Λ ; Μ, the waiting line would eventually grow infinitely large. Before using the formulas, check to be sure that Λ ; Μ.
In the single-line, multiserver, single-phase model, customers form a single line and are served by the first server available. The model assumes that there are s identical servers, the service time distribution for each server is exponential. Using these assumptions, we can describe the operating characteristics.
Performance measures are used to gain useful information about waiting line systems. These measures include:
Total time in the system or average waiting time (W): The total time waiting implies both the times spent waiting in line and also the time required for the service. The formula is, Average waiting time in line (Wq): This measure of performance deals with only the time that the customer spends waiting in line but does not includes the time required for service. This is an important measurement parameter because customers get annoyed or dissatisfied if they have to wait too long for the desired service or services. They are inclined to be less dissatisfied if the service takes long, because they know something is being done
Waiting line system is a major part in our society. Every person has had to stand in line at one point in their lives. Understanding it helps businesses compensate for these waiting periods. We recently experienced Black Friday where waiting lines were extremely long. People cutting in and disorganized lines can cause many problems. When people are finally able to shop on Black Friday, it is a rush to get to the “great deals” first. This atmosphere can cause chaos, confusion and injury. Stores like Target are understanding how important line management is to maintain order and minimizing injury. Overall, this system can be used to help reduce waiting times and where waiting times are inevitable, businesses can make the customer experience a positive one.
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