Addresses an M/M/s queueing
("waiting line") system to find s that minimizes
global cost (i.e., wait plus service)
or wait cost, in steady state.
The optimal number of servers, s,
is found by minimizing the (mean) global cost,
z(s) = Cs s + Cw L
(or wait cost,
Cs.Inactivity + Cw Lq),
from the smallest s (compatible with steady state)
until the optimum is recognized.
Other suggested data:
Cs = 6 $ h−1,
Cw = 18 h−1,
α = 40 h−1,
μ = 20 h−1 (DePaul U.)
Another example problem
[Hiller et al., 1995, Problem 16.4-10, p 752] A single crew is
provided for unloading and/or loading each truck that arrives at
the loading dock of a warehouse. These trucks arrive according to
a Poisson input process at a mean rate of 1 / h. The time required by
a crew to unload and/or load a truck has an exponential
distribution (regardless of the crew size). The expected time required
by a one-person crew is 1 h.
The cost of providing each additional member of the crew is
$ 20 per hour. The cost that is attributable to having a truck
not in use (i.e., a truck standing at the loading dock) is estimated
to be $ 30 per hour.
(a) Assume that the mean service rate of the crew is
proportional to its size. What should the size be to minimize the
expected total cost per hour ?
(b) (Not computable here) Assume that the mean service
rate of the crew is proportional to the square root of its size. What
should the size be to minimize the expected total cost
per hour ? |
|
• Hillier, Frederick, S., Gerald J. Lieberman: 2005,
"Introduction to Operations Research", 8.th ed., McGraw-Hill,
New York, NY (USA), ISBN 007-123828-X, Ch. 17, "Queueing theory";
1995, 6.th ed., ISBN 0-07-113989-3, Ch. 16, "The application of
queueing theory".
• Waiting line
models (=.pdf),
Patricia Nemetz-Mills (Eastern Washington Univ.).
• Baker, Samuel L.
(Univ. of South Carolina).
• "Dracula" (manual.pdf, (T-)junction), Inst. for Transportation Studies,
Fac. of Environment, Univ. of Leeds
(UK). |
