Chapter 12 Waiting Lines and Queuing Theory Models

1) A goal of many waiting line problems is
to help a firm find the ideal level of services that minimize the cost of
waiting and the cost of providing the service.2) One difficulty in waiting line analysis
is that it is sometimes difficult to place a value on customer waiting time.3) The goal of most waiting line problems
is to identify the service level that minimizes service cost.4) Two characteristics of arrivals are the
line length and queue discipline.5) Limited calling populations are assumed
for most queuing models.6) An “infinite calling
population” occurs when the likelihood of a new arrival depends upon the
number of past arrivals.7) On a practical note–if we were to study
the waiting lines in a hair salon that had only five chairs for patrons
waiting, we should use an infinite queue waiting line model.8) If we are studying the arrival of
automobiles at a highway toll station, we can assume an infinite calling
population.9) When looking at the arrivals at the
ticket counter of a movie theater, we can assume an unlimited queue.10) Arrivals are random when they are
dependent on one another and can be predicted.11) On a practical note–if we are using
waiting line analysis to study customers calling a telephone number for
service, balking is probably not an issue.12) On a practical note–if we are using
waiting line analysis to study cars passing through a single tollbooth,
reneging is probably not an issue.13) On a practical note–we should probably
view the checkout counters in a grocery store as a set of single channel
systems.14) A bank with a single queue to move
customers to several tellers is an example of a single-channel system.15) Service times often follow a Poisson
distribution.16) An M/M/2 model has Poisson arrivals
exponential service times and two channels.17) In a single-channel, single-phase
system, reducing the service time only reduces the total amount of time spent
in the system, not the time spent in the queue.18) The wait time for a single-channel
system is more than twice that for a two-channel system using two servers
working at the same rate as the single server. (M/M/m)19) The study of waiting lines is called
queuing theory.20) The three basic components of a
queuing process are arrivals, service facilities, and the actual waiting line.21) In the multichannel model (M/M/m), we
must assume that the average service time for all channels is the same.22) Queuing theory had its beginning in
the research work of Albert Einstein.23) The arrivals or inputs to the system
are sometimes referred to as the calling population.24) Frequently in queuing problems, the
number of arrivals per unit of time can be estimated by a probability
distribution known as the Poisson distribution.25) An (M/D/1) queuing model is classified
as probabilistic.26) An automatic car wash is an example of
a constant service time model.27) Balking customers are those who enter
the queue but then become impatient and leave without completing the
transaction.28) In a constant service time model, both
the average queue length and average waiting time are halved.29) A hospital ward with only 30 beds
could be modeled using a finite population model.
30) A finite population model differs from
an infinite population model because there is a random relationship between the
length of the queue and the arrival rate.