Waiting Line – Operations Management

Waiting Line – Operations Management

Waiting lines have become a part of everyday life. In the United States, it is estimated that Americans spend up to 37 billion hours annually waiting in lines. Whether it is waiting in lines at grocery stores to buy items by taking a number, at a bank teller, or at a cash register, a lot of time is wasted on waiting. It is a common occurrence to wait in a line at campus dining rooms, registrar’s office, movies and even food shops. The waiting time is influenced by the design of the waiting line system. A queuing system, otherwise known as a waiting line system is defined by two elements: the service system itself and the population of the customers. In this supplement, the appropriate performance measures and elements of a waiting line system will be examined. A waiting line will occur anytime there is a higher customer demand compared to the service provided. Customers will either be an inanimate object or human, but in most cases they are considered to be human (Hall, 2001). An object waiting in line to be served can be a customer waiting for an order to be processed, a machine waiting for repairs or even an electronic message on the internet. In any waiting line system, a manager has to decide the level of service to offer. A low level service in the short run will be inexpensive. However, in the long run it will incur high costs in customer dissatisfaction, actual complaints processing and loss of future business. A high level service will initially be expensive, but its results will be low dissatisfaction costs. As a result of this, the management has to consider the optimal level of service to provide.

Fast food restaurants best illustrate the transient nature of waiting line systems. During peak meal times, waiting lines are at their longest in fast food restaurants. At these hours, there is a temporary surge in demand which cannot be handled quick enough using the available resources. In an effort to ease the queues and speed up services, the restaurants normally use an extra window. The first window, for example, is utilized for paying and the second one for customers to pick their orders. When the meal hour is not at its peak, the fast food restaurants normally use one window since, at these times, there are no waiting lines at the drive-through windows. The challenge here is designing a service system with adequate as opposed to excessive capacity amounts. The fast food restaurant will experience variable demand and variable service times. There is no way for the restaurant to tell how much demand by the customer there will be; thus it is not able to tell what each customer will order. Each customer order will be unique even at times requiring a different service time. There are different elements that are involved in such a waiting line system. These elements are the service system, priorities to be used to control the line, service patterns and the customer population.

The customer population is considered to be either finite or infinite. A customer population is finite when potential new customers are influenced by the existing customers within the system. An infinite customer population is when the number of waiting customers barely affects the rate at which new customers are generated. The service system will be characterized by the number of working lines available, number of servers, their arrangement and the service priority rules. A system for the fast food restaurant can either have multiple or single lines (Hall, 2001). Banks are a good example of situations where we have a single line for their customers. The advantage of a single line is that it creates a perception of fairness among customers. A multiple line system is best when specialized servers are in use or when the space available makes it inconvenient to use the single line system. The server proficiency and the number of service facilities affect the number of servers in a system. Services will require a single activity or series of activities. These activities are identified by the term phase (Hall, 2001).

Waiting line models will require a service rate and an arrival rate. The arrival rate will specify the average customer number per period. For example, a system may have one hundred customers for every 10 hours worked in a day. On the other hand, the service rate will specify the average customer number that will be serviced during a period. The capacity of the service system is the service rate. In the case of a waiting line where the number served per period is way below average number of customers, the size of the line will continue to grow indefinitely (Albright & Winston, 2005). This means the restaurant will never catch up with the demand. To the management of this particular fast food restaurant, I would recommend the Multi-server Waiting Line model.

In a single line, single phase, multi-server model, a single line of customers would most likely ensue. They are then served by the first available server. The model makes the assumption that there are s identical servers. The service time distribution for every server is exponential. The mean service time will then be 1/U. by use of these assumptions, there is a formula that will explain the operating characteristics. The formula used to determine the operating characteristics for the multiple-server model is based on, primarily, a similar assumption as the single-server model. The assumptions are Poisson arrival rate, infinite calling population, queue rate and exponential service times, and FIFO queue discipline, however, unlike the single-server model, m > l; in the multiple-server model, sm > l. here, s is the number of servers. The formulas for operating characteristics will be as follows (Albright & Winston, 2005):

The probability that there are no customers in the system (all servers are idle) is

The probability of n customers in the queuing system is

The probability that a customer arriving in the system must wait for service (i.e., the probability that all the servers are busy) is

For this particular fast food restaurant to estimate the success of the above proposed model this is the formula they will use. It will paint a clear picture of the viability of the Multi-server Waiting Line model. Waiting lines are time consuming and at times tiring. It, therefore should be the target of the management to make it easier on the customer always. The above suggested model is best suited for this type of business. It will therefore reduce costs to the business and regulate service provision to the customer in the long and short run.


Albright, S. C. & Winston W (2005). Essentials of Practical Management Science. Mason, OH: Cengage.

Hall, R. W. (2001). Queueing Methods for Services and Manufacturing. Englewood Cliffs, N.J.: Prentice-Hall.