Step 1: Set m=0, B(0,ρ)=1

Step 2:

Step 3: Repeat Step 2 until desired value of m is reached.

Since newly arriving jobs which cannot find a free server are cleared from the system immediately, this is also referred to as a Blocked Customers Cleared (BCC) queue.

It should be noted that this queue is also of the M/M/- type with a Poisson Arrival Process and exponentially distributed service times. However, interestingly enough, the blocking probability expression given above and the state probabilities given in the earlier slide hold even if the service times have any general distribution with mean 1/μ, i.e. for a M/G/m/m queue.

M/M/1/K Queue (Single Server Queue with K-1 Waiting Positions)
   

Notice that here arrivals are allowed to enter the queue when either the queue is empty (server is free) or there are buffer positions available even though the server is currently busy. A new arrival coming when all the buffer positions become occupied (i.e. buffer is full) are forced to leave without service.               

λ_k = λ              k<K
     = 0             otherwise (Blocking or Loss Condition)

μ_k = μ             k ≤ K
     = 0            otherwise

This system is stable for ρ=λ/μ<∞ with equilibrium state probabilties p_k for k=0,1,............,K given by the following.