Transcript Capacity Planning - University of Hawaii at Hilo

Capacity Planning
Chapter 14
Capacity Planning
• Capacity planning decisions involve trade-offs
between the cost of providing a service (i.e.,
increasing the number of servers) and the cost
or inconvenience to the customer
• Involves determining the appropriate level of
service capacity by specifying the proper mix of
facilities, equipment, and labor required to meet
anticipated demand
Classification of Queuing Models
Single Server M/M/1
λ
OOOO
■
λ = arrivals per time period
O = customer
■ = server
M/M/1
Boat Launch Example
If: λ = 6 boats arrive per hour
μ = 10 boats launched per hour
p=λ/μ
Then:
probability that the customer must wait is
p = 6 / 10 = 0.6 or 60%
probability that the customer does not have to wait is
p0 = 1- 0.6 = 0.4 (40%)
M/M/1
Boat Launch Example
Mean number of boats in the system:
Ls = λ / (μ – λ)
Ls = 6 / (10 – 6) = 6/4 = 1.5 boats
Mean number of boats in the queue:
Lq = (pλ) / ((μ – λ)
Lq = (.6 x 6) / (10 – 6) = 3.6 / 4 = .9 boats
M/M/1
Boat Launch Example
Mean time in the system:
Ws = 1 / (μ – λ) = 1 / (10 – 6) = ¼ hour
Mean time in queue:
Wq = p / (μ – λ) = 0.6 / (10 – 6) = .15 hour
Multiple Servers M/M/c
■
λ
OOOO
■
λ = arrivals per time period
O = customer
■ = servers
M/M/4
Secretarial Pool Example
If: λ = 9 requests per hour
c = 4 servers
p = λ / c (used to calculate the value of p0)
Then:
probability that a faculty member does not have to wait for
secretarial work is
P0 =
1
(9/4)0 + (9/4)1 + (9/4)2 + (9/4)3 + (9/4)4
0!
1!
2!
3!
4!(1-9/16)
P0 = 0.098
M/M/4
Secretarial Pool Example
Mean number of jobs in the system:
p c+1
(P
0
Ls =
+ p)
(c-1)!(c-p)2
(9/4)5
Ls =
(0.098) + 9/4
(4-1)!(4-9/4)2
Ls = 2.56
M/M/4
Secretarial Pool Example
Mean time for each secretarial job in the system:
Ls
Ws =
λ
2.56
Ws =
= 0.28 or 17 minutes per job
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