Ch 10 - Waiting line Flashcards
Useful suggestions for managing queues based on research in the banking industry are the following:
- Segment the customers. If a group of customers need something that can be done very quickly, give them a special line so they do not have to wait for the slower customers Eg. 10 items or less self service desks.
- Train your servers to be friendly. Greeting the customer by name or providing another form of special attention can go a long way toward overcoming the negative feeling of a long wait
- Inform your customers of what to expect. - explain why the waitning is so long.
- Try to divert the customer’s attention when waiting. Providing music, a video, or some other form of entertainment may help distract the customers from the fact that they are waiting.
- Encourage customers to come during slack periods. Inform customers of times when they usually would not have to wait;
What parts does the queuing system consist of?
The queuing system consists essentially of three major components:
(1) the source population and the way customers arrive at the system,
(2) the servicing system, and
(3) the condition of the customers exiting the system (back to source population or not?)
Waiting line formulas generally require an arrival rate, what is that?
The expected number of customers that arrive each period.
A constant arrival distribution is periodic, with exactly the same time between successive arrivals. In productive systems, the only arrivals that truly approach a constant interval period are those subject to machine control. Much more common are variable (random) arrival distributions.
when arrivals at a service facility occur in a purely random fashion, a plot of the interarrival times yields an exponential distribution, what is that?
A probability distribution associated with the time between arrivals.
If the arrival process is random, the distribution is the Poisson, what is that?
Probability distribution for the number of arrivals during each time period.
Other arrival characteristics?
- Arrival patterns. The arrivals at a system are far more controllable than is generally recognized. Barbers may decrease their Saturday arrival rate (and supposedly shift it to other days of the week) by charging an extra $1 for adult haircuts or charging adult prices for children’s haircuts
- Size of arrival units. A single arrival may be thought of as one unit. A batch arrival is some multiple of the unit eg. a party of 5 at a restaurant.
- Degree of patience. A patient arrival is one who waits as long as necessary until the service facility is ready to serve him or her.
Factors to consider with waiting lines?
- line length,
- number of lines,
- queue discipline.
What is the service rate?
The number of customers a server can handle during a given time period; as the capacity of the server in number of units per time period
the flow of items to be serviced may go through a single line, multiple lines, or some mixture of the two. The choice of format depends partly on the volume of customers served and partly on the restrictions imposed by sequential requirements governing the order in which service must be performed. Which are the different line structures?
- Single channel, single phase. This is the simplest type of waiting line structure, and straightforward formulas are available to solve the problem for standard distribution patterns of arrival and service. eg. the one-person barbershop.
- Single channel, multiphase. A car wash is an illustration because a series of services (vacuuming, wetting, washing, rinsing, drying, window cleaning, and parking) is performed in a fairly uniform sequence.
- Multichannel, single phase. Tellers’ windows in a bank and checkout counters in high-volume department stores exemplify this type of structure. The difficulty with this format is that the uneven service time given each customer results in unequal speed or flow among the lines.
- Multichannel, multiphase. This case is similar to the preceding one except that two or more services are performed in sequence. The admission of patients in a hospital uses this pattern because a specific sequence of steps is usually followed: initial contact at the admissions desk, filling out forms, making identification tags, obtaining a room assignment, escorting the patient to the room, and so forth. Because several servers are usually available for this procedure, more than one patient at a time may be processed.
- Mixed. Under this general heading, we consider two subcategories: (1) multiple-tosingle channel structures and (2) alternative path structures. Under (1), we find either lines that merge into one for single-phase service, as at a bridge crossing where two lanes merge into one, or lines that merge into one for multiphase service, such as subassembly lines feeding into a main line. Under (2), we encounter two structures that differ in directional flow requirements. The first is similar to the multichannel– multiphase case, except that (a) there may be switching from one channel to the next after the first service has been rendered and (b) the number of channels and phases may vary—again—after performance of the first service.
Once a customer is served, two exit fates are possible:
(1) The customer may return to the source population and immediately become a competing candidate for service again or (2) there may be a low probability of reservice. The first case can be illustrated by a customer machine that has been routinely repaired and returned to duty but may break down again; the second can be illustrated by a customer machine that has been overhauled or modified and has a low probability of reservice over the near future.
Which are the 4 waiting line problems?
Problem 1: Customers in line.
Problem 2: Equipment selection.
Problem 3: Determining the number of servers.
Problem 4: Finite population source.
