Question

A queue with one server without buffer, the probability of a customer’ arrival and departure in a time unit is p and q respectively. Please try to 1) give the one step state transition probability matrix. 2) give the balance equations. 3) calculate the limiting probabilities for p=0.3 and q=0.5. (12 points)

Answer 1

Answer:

Given that:

A queue with one server without buffer, the probability of a customer’ arrival and departure in a time unit is p and q respectively.

for M/M/1 queue

The transition probability matrix for an M/D/1 queue with arrival rate p and service time 1,such that p<1 (for ability of the queue) is given by p as below

Balance equations:

At state 0 : (or)

At state n:

At state k:

  

Where

N=average number of customers in system