# Simple queue

• March 24th 2010, 09:41 AM
Anonymous1
Simple queue
Consider the queue: Customer $\rightarrow S_1 \rightarrow S_2 \rightarrow$ leave.

Customers arrive at rate $2;$ $S_1$ serves at rate $4;$ $S_2$ serves at rate $2.$

If a customer comes to an occupied server he leaves the system.

Formulate a markov chain model for this system with state space $\{0,1,2,12\}$ where the states indicate the servers who are busy.

$(a)$In the long run what proportion of customers enter the system? (If a customer leaves before being served by $S_1$ he does not enter)
$(b)$What proportion of customers visit server $2?$