Queueing Theory Calculator

Queuing Theory Model
1. Choose the queueing model.

Single queue, C servers.

At least one server per customer.

Queue can only hold K customers.

Only M customers can use the server.

Comments / Instructions
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Instructions – How to use the queuing theory calculator

The following instructions are meant for the Queuing Theory Calculator at

Quick Start

If you are familiar with queueing theory, and you want to make fast calculations then this guide can help you greatly.

  1. Choose the queuing model you want to calculate. M/M/C (or M/M1 if you put C=1), M/M/Inf, M/M/C/K, or M/M/C/*/M
  2. Then chose the number of servers in your system (C), the maximum number of entities (aka. Customers) that your queue can hold (K), and the maximum number of entities that exist in your entire population (M).
  3. Choose the arrival (Lambda) and service rates (Mu). Notice there is an option for setting your units, in practice you can find out that the arrival and the service rates defer in units. This calculator can help managing that and converting the units of Lambda and Mu to other ones.
  4. Press Calculate.
  5. Get the answers for server utilisation (Ro), Average entities in the whole system (L), Average entities in queue (Lq), Average time an entity spends in the system (W), Average time an entity waits in line to be served (Wq), Lambda prime (Lambdap), the probability of being be exactly 'n' entities in the system at a certain point (Pn) (modify the value of 'n' as desired), the probability of an entity will spend exactly or less than 'n' units of time in the queue (Tq) and the probability of an entity spending exactly or less than 'n' units of time in the system (T), service time plus queuing time .

I hope it helps!
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