The Mathematical Garden

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Mathematical methods
HMMs
Mathematical Induction
Pigeonhole principle
Random Walk
Gambler's Ruin
An Analysis of the Problem
A Greedy Gambler
A Greedy Gambler Simulation
An One-server Queueing System
An Analysis of the Problem
Performance of the Queueing system
Infinite Waiting Space Queue
Solving Linear Systems

Performance of the Queueing system

The probability that the server is idle is given by r0.

The probability that the queue is full and an arrived customer is rejected by the system is given by rN.

The expected number of customers at the server is given by

0 x r0 + 1 x   N
S
i=1
  ri = 1 - r0.

The expected number of customers in the system is given by

N
S
i=1
  i x ri.

Department of Mathematics, HKU, 2010