advertisement

Modeling & Simulation- Lecture -5- 12/11/2014 Solving Queuing models: 1 single queue The state diagram of birth-death process for M / M / 1 λ λ 0 1 µ λ 3 2 µ λ µ µ We have balanced equations: the probability flow out of a state = the probability flow into that state . We can rewrite these as shown below: Remembering that traffic intensity, 𝜌= 1 𝜆 µ For the single server Lecturer: Hawraa Sh. Modeling & Simulation- Lecture -5𝜌= 𝜆 𝑐×µ 12/11/2014 For multi-server Then we can see that for any 𝑥𝑖 And after using normalization condition we see that: From this the steady state of M/M/1 can be as: Some performance measurement of M/M/1 : Utilisation, U the queue is being utiliesd whenever it is non-empty this mean: Mean number of entity in the queue, N , the entity in service facility: 2 Lecturer: Hawraa Sh. Modeling & Simulation- Lecture -5- 12/11/2014 Mean number of entity waiting , 𝑵𝒃 this the number of entity in the buffer : Mean Response time, R, 3 Lecturer: Hawraa Sh. Modeling & Simulation- Lecture -5- 12/11/2014 Some examples for common performance measurements shown in table below: 4 Lecturer: Hawraa Sh.