# Analyzing Waiting Lines

Topics: Normal distribution, Poisson distribution, Probability theory Pages: 11 (3027 words) Published: May 28, 2013
Analyzing Waiting Lines

Most people find waiting lines irritating – waiting is idle and nonproductive time. From a service system perspective, however, a line represents a demand for service.

Think of a restaurant on a Friday night. As a customer it is an irritation to have to wait 40 plus minutes for a table, but from the restaurant’s perspective, if there is not a line, then that means there are empty tables. Idle services are not good.

So management must balance waiting time with the resources used to provide a service. Health administrators face a duel and potentially conflicting concern. On the one hand, health administrators are concerned about efficiency and worker productivity. Idle staff, machines, and surgical suites benefit neither the organization, the organization’s financial position, nor its potential patients or clients. On the other hand, health administrators want their organization and its staff to be able to provide a quality service when it is needed. Administrators want to minimize, for example, the amount of time a patient must wait for surgery a lab test, or a specific treatment. Delay in providing a service is never good. Long delays may lead to a change or deterioration in the condition of the patient or a lab specimen awaiting a test.

To have an efficient organization as well as efficient service systems and subsystems, managers must balance acceptable waiting times with the input resources used to provide the service. This balancing can be referred to as managing the service system.

Cost of providing the service. This is also known as service cost. Examples include wages paid to servers, the cost of buying an extra machine, and the cost of constructing a new teller window. As a firm increases the size of its staff and provides added service facilities, the result could be excellent customer service with seldom more than one or two customers in a queue. While customers may be happy with the quick response, the cost of providing this service can, however, become very expensive.

Cost of not providing the service. This is also known as the waiting costs and is typically the cost of customer dissatisfaction. If a facility has just a minimum number of checkout lines, pumps, or teller windows open, the service costs is kept low, but customers may end up with long waiting times in the queue. As the average length of the queue increases and poor service results, customers and goodwill may be lost.

This is illustrated graphically below. The costs of waiting are tough to measure of course, and so this is a conceptual idea. There is, however, an optimal level of service that balances these costs.

Compare this to Six Sigma?

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Many analytical models exist to assist the manager in analyzing service systems and balancing the capacity of the system to provide a unit of service with the time a unit must wait for service. Some of these models can be found in Queuing Theory, the formal study of waiting lines.

Defining Characteristics of Waiting Lines

Random Arrivals – refers to unscheduled arrivals that are not influenced by when previous units arrived or left. If the average number of units that arrive in 1 hour is six, this does not mean that a unit arrives every 10 minutes. It means that in any 1 hour, six units on average will arrive. Random arrivals mean that probabilities govern when units will arrive in the specified time period.

FIFO Line Behavior – this means first in, first out. Ina FIFO situation, the order of service is determined by the order of arrival. Hospital emergency rooms do not use FIFO; here the need for stat (from the Latin statim, or immediately) servicing of some units can change any FIFO system for one specific case or situation.

Channels and Servers – The number of channels refers to the number of servers available to arriving units. Some systems are designed to have a single channel, and other...