MA213 Flashcards
arrival rate
A
serving rate
y
traffic intensity
p = A/y
steady system
(1-p)p^n
probability that the server is idle
po = 1-p
pr that server is busy
p
expected no of customers served
p
expected no of customers in the system
Ls = p/1-p
expected time in the system
Ls/A
expected no. of customers in the queue
Lq = p^2/1-p
expected queuing time
Lq/A
expected queuing + service time
Lq/A
conditional expected queuing time (given that there’s already a queue)
1/y-A
expected proportion of idle time per server
(1-n/s)Pn
expected number in the queue
Lq = po . sp/s! . p/(1-p)^2
expected waiting time in the queue
Lq/A
expected no of customers being served
A/y
F(S*)
p-c/p+h
Optimal service level F(X*)
Cu/Co+Cu
Reorder point
P(X>R) = q
R = F-1(q)
e.g. y=30, o=0.3, q=0.05, N(0,1)
F(r) = 0.95 so r = 1.65
R = y + ro = 30 + 1.65(0.3) = 34.95 so the reorder point is 35
Q* with planned shortages
Q* = sq root. 2dk/h . p+h/p
S* with planned shortages
S* = sq. root 2dk/h . p/p+h
t*
Q*/d
Q*
sq.root 2dk/h
