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
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!