Queuing and Waiting Theory
•n = number of servers.
•λ = arrival rate of customers (Poisson input).
•∝ = service rate for each server (exponential service).
•ρ = Intensity factor = λ / ∝ (ρ, n for valid results).
•P0 = Probability that all servers are idle.
•Pb = Probability that all servers are busy.
•Lq = Average number of customers in queue.
•L = Average number of customers in the system (waiting and being served).
•Tq = Average waiting time in queue.
•T = Average total time through the sytem.
•P(t) = Probability of waiting longer than time t.
•
P0 =
n – 1 |
| ρn |
ρk |
| |
+ | ||
∑k! | n! | 1 – |
k = 0 | | n |
|
| |
•
P |
|
| ρnP0 | |
b | = | |||
| n! | | ρ | |
|
| | 1 – | |
|
|
| n | |
•
•
Lq | ρPb | L = L |
| + ρ | T = L / λ | T |
| Lq |
= | q | q | = | |||||
| n – ρ |
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|
|
| λ |
•P(t) =
