General system notations

a: Arrival distribution

• M : Markovian/Poission arrival distribution

• D : Constant/Deterministic time of arrival

• : Erlang/Gamma distribution of time of arrival (sum of n number of exponential distribution is Gamma distribution)

• GI: General distribution for interval arrival time

b: Departure/Service time distribution

• M: Markovian/Poission departure/service distribution

• D: Constant/Deterministic departure/service time

• : Erlang/Gamma distribution of time of departure/service (sum of n number of exponential distribution is Gamma distribution)

• G: General distribution for departure/service time

c:Number of parallel servers, , (in general the number can be 1, 2,…,  )

d: Queue discipline

• FIFO/FCFS: First in first out or first come first server

• LIFO/LCFS: Last in first out or last come first server

• SIRO: Service in random order

• GD: General discipline (e.g., with priorities, weightages, etc.)

e: The maximum number of customers allowed in the system (remember it is the number being served by     server system plus the number standing in the queue system)

f : The size of the calling source, i.e., from where the customers are coming and joining the queue.

So for example (M/M/3):(FIFO/25/500) would imply that we have

(i) M: Markovian/Poission arrival distribution
(ii) M: Markovian/Poission departure/service distribution
(iii) Number of servers is 3
(iv) We have the discipline of the queue as first in first out
(v)  Maximum number of customers allowed in the system is 25
(vi) The size of the outside source from where customers are joining the queue is finite in number and is           500