Industrial engineering and operations research / Basic Queueing Theory - I

Queueing theory: It is a mathematical approach to calculate queue lengths ( number of customer in the queue ) and waiting time for the customer. In queueing theory a model is constructed so that queue lengths and waiting time can be predicted. 

Service Discipline or service Rules :  The order in which customers are being served, determines the service discipline or service Rule. Some of the common service disciplines in use are,

•        FIFO  :  First In First Out    

•       FCFS : First Come First Served

•        LIFO : Last In First Out 

•       SIRO : Service In Random Order

Notation used to describe queueing system is denoted as   (a:b:c) : (d:e:f) a = Arrival Pattern                            b = Service pattern c = Number of server d = Service rule e = Maximum number of customer in system f  = Population

Model : 01

(M/M/1) : (∞/FIFO)  -  The notation denotes a queueing model in which 

• Arrival of customers is generated by poison distributed (inter arrival time is exponentially distributed)

• Service time is exponentially distributed

• Number of server is one

• The size of population is infinite

• Service rule is FIFO

λ = Mean arrival rate i.e. Number of customer coming in the system per unit time

µ = Mean service rate i.e. Number of customer served per unit time

Note :- For single server system it is assumed that µ ≥ λ . If λ < µ then queue will be never ending queue or infinite queue.

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