S-38.149: Special course in teletraffic theory.

Homework due on November 2, 1998.

Philip Ginzboorg

Local calls enter a PBX (vaihde) through interface cards. A card monitors the state of its telephone lines and connects a dial tone to links that are in the off-hook state. We model the interface card as two M/M/1 queues in tandem (see Figure 1). We denote by i the number of calls in the first queue, including the call in the server, and by k the number of calls in the second queue. The capacity of the first queue is W and the capacity of the second queue is N. A call gets a dial tone when it leaves the second queue.

Assume m₁ = 101 [calls/s], m₂ = 1 [call/s], W = 3 and N = 2.

• (a) Draw the state diagram showing all the transition rates.
• (b) Write the equilibrium equations (such as p(0,0) l = p(0,1) m₂) of the system.

And finally, given that l = 0.9 [calls/s], estimate

• (c) the probability of call blocking,
• (d) the average dial tone delay.