For cost analysis in queueing, the goal is to minimize what two costs?

The Basics of Queuing Theory

Queuing theory is essentially a vehicle for cost analysis. It would be prohibitively expensive, or indicative of not having very many customers, for most businesses to operate in a manner so that none of their customers or clients ever had to wait in line. As a simplistic example, for a movie theater to eliminate the circumstance of people having to wait in line to purchase a movie ticket, it would likely need to set up fifty to a hundred ticket booths. However, the theater obviously could not afford to pay a hundred ticket sellers.

Therefore, businesses use information gleaned from queuing theory in order to set up their operational functions so as to strike a balance between the cost of servicing customers and the inconvenience to customers caused by having to wait in line.

The basics of queuing include the people waiting in line and the performance of the service that they’re waiting to receive. In studies on queuing, it is usually broken down into four categories, as follows:

• Arrival – The process by which customers arrive at the line/queue
• The Queue – The nature or operation of the queue itself (How does the line move along?)
• Service – The process of providing the service that a customer is waiting on (for example, being seated and then being served in a restaurant – note that the restaurant has to consider the dynamics of two separate queues, the queue of people waiting to be seated, and then the queue of people already seated who are waiting to be served. The latter might be further broken down into the two queues of waiting to have your order taken and waiting for your food to arrive at your table).
• Leaving – The process of departing from the queue location (for example, businesses that offer a drive-through service have to consider how people leaving the drive-through may impact people entering the business’ parking lot)

Factors of Queuing – Arrival

Queuing models analyze the operational aspects and variables involved in each of the four categories of queuing outlined above. Following are some of the variables that can affect the functioning and operational efficiency of each part of a queue, and that, therefore, should be considered by the business where a queue forms.

Factors to consider in relation to the arrival of people at the queuing location include such things as the number of people, on average, who arrive within a given time frame, such as one hour. A related factor is that of substantial fluctuations in the amount of traffic/arrivals that occurs at different times of the day and/or on different days of the week or month.

Grocery stores know, for example, that in order to avoid queues getting backed up, they need to have more employees working during rush hour on a Friday than, say, on Wednesday mornings between 10 a.m. and noon.

Factors of Queuing – The Queue

How does the line move along? For example, does it work better for a bank to have just one line of customers waiting for the next available teller or cashier, or to have separate lines for each teller? Characteristics of human behavior become an important part of queuing theory when posing such a question. While one line of customers being fed to four different teller stations versus four separate lines at each teller station may not have a significant effect on how quickly or efficiently customers are served, it may well have an impact on customer satisfaction.

Although ultimately, the wait time to be served may be roughly the same regardless of the line arrangement, customers may feel, or perceive, that they are being served more quickly if they only have to wait in line behind two or three people (each teller station has its own queue) as opposed to having to stand in line behind 10 or 12 people (one line of customers being fed to all four teller stations).

There are also basic practicalities to consider: If the business office is relatively small, will using just a single line result in a line so long that it extends back out the door? Many people seeing a situation like that may well be discouraged from doing business there. They may instead choose to go to a competitor that appears to offer less wait time.

Note the part about “appears” to offer less wait time. Doing business with the competitor may, in fact, involve approximately the same amount of time waiting in line. The only difference may be that the competitor chose to go with separate lines for each service station rather than one single line for all the stations, thus avoiding having a line that extends back out the door. Here, you can see that there are aesthetics of queues to be considered in addition to any operational efficiency factors.

Factors of Queuing – Service

There are also variables that exist in relation to the actual provision of service. A common example is the “express lane” in grocery stores, reserved for customers who are only purchasing a small number of items. (Typically, express lanes are designated for customers with “12 items or less” or “20 items or less”). The reason such express lanes exist is that grocery stores using queuing theory have found that customer satisfaction is improved by enabling customers who are only buying a few things to check out more quickly, as opposed to having to wait in line behind other customers with full carts of groceries.

Other factors that impact actually providing service include how long, on average, it takes to provide service to each customer or client, the number of servers required for maximum operational and cost efficiency, and the rules governing the order in which customers are served. While most queues operate on a “first-come, first-served” basis, it is not appropriate for some businesses.

A classic example is the waiting area at a hospital emergency room. Rather than using a “first arrival” basis for service orders, patients are served based on the severity of their illness or injury. It necessitates adding a service step known as “triage,” whereby a nurse evaluates each patient in terms of the severity of their emergency to decide where in the line of receiving service that patient is placed.

Factors of Queuing – Leaving

The elements associated with customers departing a queue location are commonly basic logistical matters. The example was related above of how businesses with drive-through operations have to take into account how people leaving the drive-through may affect incoming traffic to the location.

Another example of a departure-related factor is a restaurant determining whether to have servers present bills and collect payment at a customer’s table or to have customers pay their bill to a cashier on their way out.

More Resources

CFI offers the Commercial Banking & Credit Analyst (CBCA)™ certification program for those looking to take their careers to the next level. To keep learning and developing your knowledge base, please explore the additional relevant resources below:

• Decision Analysis
• Operations Management
• Demand Theory
• Logistics

Chapter 18 Objectives

1. Planning and analysis of service capacity frequently lends itself to queuing theory, which is a mathematical approach to analysis of waiting lines.

·        The foundation of modern queuing theory is based on studies about automatic dialing equipment made in the early part of twentieth century by Danish telephone engineer A.K. Erlang

·        One reason that queuing analysis is important is that customers regard waiting as non-value added activity

·        Managers have a number of very good reasons to be concerned with waiting lines. Chief among those reasons are the following:-

1. The cost to provide waiting space.
2. A possible loss of business should customers leave the line before being served or refuse to wait at all.
3. A possible loss of good will.
4. A possible reduction in customer satisfaction.
5. The resulting congestion may disturb other business operations and/ or customers.
6.  
1. The goal of queuing is essentially to minimize total costs

·        The two basic categories of cost in a queuing situation are: -

1.      Those associate with customers waiting for service and

2.      Those associate with capacity.

·        Capacity costs are the costs of maintaining the ability to provide services. Examples include the number of bays at a carwash, the number of checkouts at a supermarket and the number of line on the highway.

·        The cost of customer waiting includes the salaries paid to employees while the wait for service (mechanic waiting for tools, the drivers of trucks waiting to unload).

1. The traditional goal of queuing analysis is to balance the cost of providing a level of service capacity with the cost of customers waiting for services.
2. There are numerous queuing models from which an analyst can choose. Model choice is affected by the characteristics of the system under investigation. The main characteristics are: -
1. Population source.
2. Number of servers (channels)
3. Arrival and service patterns.
4. Queue discipline (order of service)

1.      Population source:- the approach to use the analyzing a queuing problem depends on whether the potential number of customers is limited. There are two possibilities: infinite source and finite source

·        Infinite source:- customer arrivals are unrestricted.

·        Finite source:- the number of potential customers is limited.

2.      Number of servers (channels): - the capacity of queuing systems is a function of the capacity of each server and number of servers being used. System can be either single or multiple-channel. (a group of servers working together as a team, such as a surgical team, is treated as a single channel system.)

Examples of single-channel systems are small grocery, stores with one checkout customer, some theaters, single bay carwashes and drive-in banks with one teller. Multiple-channel systems (those with more than one server) are commonly found in banks, at airline ticket counters, and auto service center, and gas stations.

3.      Arrival and service patterns: - waiting lines are a direct result of arrival and service variability.

4.      Queue discipline:- refers to the order in which customers are processed.

5. The operations manager typically looks at five measures when evaluating existing or proposed service systems. These measures are: -

1.      The average number of customers waiting, either in line or in the system

2.      The average time customers wait, either in line or in the system.

3.      System utilization, which refers to the percentage of capacity utilized.

4.      The implied cost of a given level of capacity and related waiting line.

5.      The probability that an arrival will have to wait for service.

6.       

6. Many queuing models are available for a manager or analyst to choose from. The most basic and most widely used models are: -

·        Single channel, exponential service time.

·        Single channel, constant service time.

·        Multiple channel, exponential service time.

·        Multiple priority service, exponential service time.

1. Single channel, exponential service time: - the simplest model involves a system that has one server (or a single crew). The queue discipline is first-come, first served, and it is assumed that the customer arrival rate can be approximated by a Poisson distribution and service time by a negative exponential distribution
2. Single channel, constant service time. The effect of a constant service time is to cut in half the average number of customers waiting line.
3. Multiple channel: - A multiple channel system exists whenever there are two or more servers working independently to provide service to customer arrivals. Use the model involves the following assumptions:

1.      A Poisson arrival rate and exponential service time.

2.      Servers all work at the same average rate.

3.      Customers form a single waiting line(in order to maintain first-come, first-served processing).

4. Multiple priorities: - customers are processed according to some measure of importance. (e.g. hospital emergency waiting room).