Simulated 1000 customers
Average wait time : 0.4640
Average sojourn time : 1.1262
Server utilization : 0.6667 (theoretical)
15 M/M/n Queue
The M/M/n queue is a discrete stochastic process that models a queue with n servers. There are three parameters:
- \(n\): the number of servers
- \(\lambda\): the arrival rate of customers
- \(\mu\): the service rate of each server
The “M” in M/M/n stands for “memoryless” or Markovian. The M/M/n queue models the following process: - customers arrive at the queue according to a Poisson process with rate \(\lambda\). - Each customer is served by one of the n servers, and the service times are exponentially distributed with rate \(\mu\). - If all servers are busy, the customer waits in line until a server becomes available.
We are interested in testing the performance of the queue as function of the three parameters. There are various performance measures we can compute, including: - The average number of customers in the waiting line - The average time a customer spends waiting in line - The usage of the servers - The probability that a customer has to wait in line
There are two approaches we can take to simulate an M/M/n queue
- Process driven
- Event driven