The Finite Buffer Case: M/M/1/N

• Infinite buffer assumption is unrealistic in practice.

• N = total number of buffer slots (including server).

• New state diagram:

  

• Get the same balance equations

• But now for .
• So

  

• From , for , and , we get

  

• So

  

• Note that this holds for any .
• No need to assume .
• We always have stability in finite buffer case.

• Blocking Probability and the Right Size Buffer
• Throughput in the Finite Buffer Case
  • Alternate way to compute throughput of M/M/1/N: Look at the output side
  • Aside: Derivation of = Using Throughput
• Approximation of a Finite Buffer System by the Infinite Buffer Model