What is QUEUE?
Any system where jobs arrive looking for service and
depart once service is provided is described as a
The Queuing theory provides predictions about
waiting times, the average number of waiting
customers, the length of a busy period and so forth.
System Customers Server
Reception desk People Receptionist
Hospital Patients Nurses
Airport Airplanes Runway
Road network Cars Traffic light
Grocery Shoppers Checkout station
Computer Jobs CPU, disk, CD
Assumptions of M/M/1 Queuing System
The number of customers in the system is very large.
Impact of a single customer on the performance of
the system is very small.
All customers are independent.
A single server for the queue.
The queue discipline for this system is FIFO.
•t is used to define the interval 0 to t
•n is the total number of arrivals in the interval
0 to t.
•lambda is the total average arrival rate in
Cars On a
Consider a highway
with an average of 1 car
arriving every 10
rate). The probability
distribution with t is
ρ = λ / µ
•rho is occupancy (traffic intensity)
•mu is average service rate.
•N is mean number of customers.
•T is total waiting time.