Business Analytics Module #4 Exam (Ch. 13 & 14)

The constant service time model

A special case of a more general variation of the single-server model in which service times cannot be assumed to be exponentially distributed. As such, service times are said to be general, or undefined. - There is no variability in service times.

The Monte Carlo technique

A technique for selecting numbers randomly from a probability distribution (i.e., "sampling") for use in a trial (computer) run of a simulation. - Not a simulation model but rather a mathematical process used within a simulation.

A finite calling population

For some waiting line systems there is a specific, limited number of potential customers that can arrive at the service facility. What is this referred to as?

finite

For some waiting line systems, the length of the queue may be limited by the physical area in which the queue forms; space may permit only a limited number of customers to enter the queue. Such a waiting line is referred to as a __________ queue.

An automatic car wash can accommodate one car at a time, and it requires a constant time of 4.5 minutes for a wash (60/4.5 = 13.3 cars per hr.)

Give an example of the single-server model with constant service times.

A business has a single fax machine. The time an employee spends using the machine is not defined by any probability distribution but has a mean of 2 minutes and a standard deviation of 4 minutes.

Give an example of the single-server model with general, or undefined, service times.

negative exponential probability

It has been determined by researchers in the field of queuing that service times can frequently be defined by a __________ __________ __________ distribution.

Poisson

It has been determined that the number of arrivals per unit of time at a service facility can frequently be defined by a __________ distribution (a type of probability distribution).

Overview of Waiting Line Analysis: - People, products, machinery, planes, etc. spend a significant portion of time waiting in lines. - Customers increasingly equate quality service with rapid service. - The basis of waiting line analysis is the trade-off between the cost of improved service and the cost of making customers wait. - Like decision analysis, queuing analysis is a probabilistic form of analysis, not a deterministic technique. Thus, the results of QA, referred to as operating characteristics (OCs), are probabilistic. These OCs (such as the average time a person must wait in line to be served) are used by the manager of the operation containing the queue to make decisions. Elements of Waiting Line Analysis: - Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served. - Does this mean that the service operation is understaffed? No. - Does this mean that the service operation does not have the overall capacity to handle the influx of customers? No. - If the service operation is not understaffed and has sufficient overall capacity, then why do waiting lines result? Because customers do not arrive at a constant, evenly paced rate, nor are they all served in an equal amount of time (i.e., variable arrival and service rates). - A waiting line is continually increasing and decreasing in length, and it approaches an average rate of customer arrivals and an average time to serve the customer in the long run. - Decisions about waiting lines and the management of waiting lines are based on these averages for customer arrivals and service times. They are used in queuing formulas to compute OCs, such as the average number of customers waiting in line and the average time a customer must wait in line.

Provide an overview and discuss elements associated with waiting line (queuing) analysis.

steady state

Queuing system operating characteristics are assumed to be __________ __________ averages.

L

The average number of customers in the queuing system (i.e., the customers being serviced and in the waiting line)

Lq

The average number of customers in the waiting line

W

The average time a customer spends in the total queuing system (i.e., waiting and being served)

Wq

The average time a customer spends waiting in the queue to be served

Pn

The probability that n customers are in the queuing system

P0

The probability that no customers are in the queuing system (either in the queue or being served)

U

The probability that the server is busy

The utilization factor

The probability that the server is busy (i.e., the probability that a customer has to wait)

I

The probability that the server is idle (i.e., the probability that a customer can be served)

The calling population

The source of customers; it may be infinite or finite. Queuing systems that have an assumed infinite calling population are more common.

Multiple-server model

Two or more independent servers in parallel serve a single waiting line. - Ex: An airline ticket and check-in counter where passengers line up in a single line, waiting for one of several agents for service.

1. An infinite calling population 2. A first-come, first-served queue discipline 3. Poisson arrival rate 4. Exponential service times

What are the assumptions of the basic single-server model?

1. The queue discipline (in what order customers are served) 2. The nature of the calling population (where customers come from) 3. The arrival rate (how often customers arrive at the queue) 4. The service rate (how fast customers are served)

What are the most important factors to consider in analyzing a queuing system?

To generate a random variable (e.g., demand) by sampling from its probability distribution.

What is the purpose of the Monte Carlo process?

A service rate is similar to an arrival rate in that it is a random variable. In other words, various factors alter the number of persons that can be served over time. Arrivals are described in terms of a rate and of service, in terms of time. However, to analyze a queuing system, both arrivals and service must be in compatible units of measure. Thus, service time must be expressed as a service rate to correspond with an arrival rate.

What is the relationship between arrival and service rates?