hp 12c_solutions handbook_English_E

163
Queuing and Waiting Theory
• n = number of servers.
• λ = arrival rate of customers (Poisson input).
• µ = service rate for each server (exponential service).
• ρ = Intensity factor = λ / µ (ρ, n for valid results).
• P
0
= Probability that all servers are idle.
• P
b
= Probability that all servers are busy.
• L
q
= Average number of customers in queue.
• L = Average number of customers in the system (waiting and being
served).
• T
q
= Average waiting time in queue.
• T = Average total time through the sytem.
• P(t) = Probability of waiting longer than time t.
•
•
•
•
• P(t) = P
b
e
-(n
µ - λ
)t
Graduated Payment Mortgage
P
0
ρ
k
k!
-----
k0=
n1–
∑
ρ
n
n! 1
ρ
n
---
–


------------------------+
1–
=
P
b
ρ
n
P
0
n! 1
ρ
n
---
–


------------------------=
L
q
ρ P
b
n ρ –
------------=
LL
q
ρ +=
T
q
L
q
λ
------=
T = L / λ