# Queueing Theory Calculator

From IFORS Education Resources

**Quick Start**

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

- 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

- Then chose the number of servers in your system (C), the maximum number of entities that your queue can hold (K), and the maximum number of entities that exist in your entire population (M).

- Choose the incoming (Lambda) and service rates (Mu). Notice that there is an option for units, in practice you sometimes get the incoming and the service rates with different units. This calculator helps with that by converting the units of Lambda to those of Mu. You can also input the hours a day that your system should work. Eg. A bank that works from 8 a.m. to 3 p.m. will have to consider 7 hours per day in their calculations.

- Press Calculate.

- 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 that there would be exactly 'n' entities in the system at a certain point (Pn) (modify the value of 'n' as desired), the probability that an entity will spend in line exactly or less than 'n' units of time (Tq) and the probability that an entity will spend exactly or less than 'n' units of time in total in the system (T).

- You can make quick calculations on the given “space for calculations” by inputing the desired formula an then pressing the 'Res' button. E.g. input '2+2' then [Res] it will display 4. Note: al the above symbols in '( )', for instance 'C', 'K', 'M', etc. can also be used. E.g. 'T^2+Ro' Should give you an answer, or '1-T' should give you the probability that an entity will spend more than 'T' units of time.

- I hope it helps.

**Link to material:** http://www.supositorio.com/rcalc/rcalclite.htm