Queuing Tutorial

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M/M/s/N/N Queuing System

In this model of queuing system, the arrival distribution of customers follows Poisson distribution and the distribution for service time follows Exponential distribution with s number of parallel servers. The number of population and the queuing capacity is limited to N. This situation often happens in queuing for machine repair system where the number of population is equal to the number of machine = N.

Use the M/M/s/N/N queuing calculator below to experiment and to solve queuing problem of multiple parallel servers with queuing capacity N. Compare it with M/M/s and M/M/s/N queuing system.

The performance for M/M/s/N/N queuing system are given by the formulas below.

Input:

  • Arrival rate (number of customers/unit time) Machine Repair Queuing System
  • Service rate (number of customers/unit time) Machine Repair Queuing System
  • Number of servers Machine Repair Queuing System
  • Capacity of the system = limited population = Machine Repair Queuing System ; maximum queue size = Machine Repair Queuing System

Output:

  • U= operative Utilization = Machine Repair Queuing System
  • P 0 = probability that there are no customers in the system, Machine Repair Queuing System
  • P n = probability that there are n customers in the system, Machine Repair Queuing System
  • W q = average time a customer spends in waiting line waiting for service, Machine Repair Queuing System Machine Repair Queuing System
  • W = average time a customer spends in the system (in waiting line and being served), Machine Repair Queuing System
  • L q = average number of customer in waiting line for service, Machine Repair Queuing System
  • L = average number of customer in the system (in waiting line and being served), Machine Repair Queuing System
  • Machine availability Machine Repair Queuing System


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These tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi. (2014) Queuing Theory Tutorial
http://people.revoledu.com/kardi/tutorial/Queuing/