Queueing Network Demo

Brief Descriptions of Example Models

M/M/1 queue is probably the most common queuing model. The Poisson source is served by one server with infinite waiting places (applet has finite capacity of 100, which is in practice never reached).
Traffic parameters are λ=0.08 and μ=0.15, hence offered load ρ=8/15.
Erlang(3,1) model shows the standard Erlang system with 3 servers and no waiting places. The customers arriving to full system overflow and are shown at upper overflow delay line, while served customers appear on lower delay line. The the traffic parameters are λ=μ=0.15, and thus the blocking probability is

Erl(n,a) = Erl(3,1) = 6.25%.
Closed Network consists of two identical M/M/1 queues connected as a ring. From a finite source ten customers are guided to the system, where they move from one queue to another.
Shared servers is an example trying to demonstrate the performance difference between three system having equal processing power. The same work flow is first duplicated to three identical streams.
- System 1 consists of single server which processing speed is 1.0,
- System 2 has two servers processing at speed of 0.5, and
- System 3 first splits the input randomly to two streams which are served by two identical servers with processing speeds of 0.5.
The performance of each queue can be studied by comparing the average delays customers experience at the system. Note that the average waiting time shown in popup window of processor does not include service time. So in this case where μ=0.15 you must add about 6.7 to waiting time of System 1, and about 13.3 to waiting time of System 2 and System 3, to get the total delay customer entering the system experiences.

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Esa Hyytiä, 2001.