The Optimization Model of Campus Network Port Resources Based on Queuing Theory - Advanced Research on Computer Education, Simulation and Modeling - page 49

In summary, the service system is real-time queuing system for more than a desk.
According to the changes of input process, queuing rules and service mechanism, by
analyzing the information we can know that the problem with queuing model with
Ken Doyle (D.G.Kendall) proposed currently in queuing theory widely used in
"Kendall mark" can be represented by

MMnn ∞ / ///

.
According to the meaning of problems, each user on an average day time online
1.5 hours, subscribers 150 person, can be given time unit of subscribers for 150/16
people/hour.

()

N t Process is a thickening and elimination process which has the
following parameter:

μμ
λλ
λ

= k

⎧ ⎪

k

= kn

kn

≤

⎨
⎪

(1)

k

= 0 >

⎩

k

MMnn / /// ∞

Fig. 1. system state probability distribution and state transfer speed

diagram

Assuming the system state is k (ie k users on the Internet) the probability is P ,
from this figure we can easy to get: Transfer rate = transfer out rate, steady-state
probability should satisfy the relationship:

⎧
⎪

λμ
λ

PP
P

=

⎪ ⎪

0 1

= μ P (2)

⎨
⎪
⎪

k − 1 k

n

⎪ ⎩ ∑

P = 1

k

k = 0

According to the recursive formula can be solved:

k

1
!

⎛⎞ λ

μ

P

= P

(3)

⎜ ⎝⎠

0

k

− 1

⎡

k

⎤

n

⎛⎞

1
!

λ
μ

λ

∑

P = ρ =

⎢ ⎥

Among them , .Then steady-state solution is:

⎜ ⎝⎠

0

μ

k

⎢ ⎥

⎣ ⎦

k = 0