Components of Queuing System
- Input Source: The input source generates customers for the
service mechanism. The most important characteristic of the input
source is its size. It may be either finite or infinite. Please note
that the calculations are far easier for the infinite case, therefore,
this assumption is often made even when the actual size is relatively
large. If the population size is finite, then the analysis of queuing
model becomes more involved.
The statistical pattern by which calling units are generated over
time must also be specified. It may be Poisson or Exponential probability
distribution.
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Usually the source population is considered
as unlimited. |
- Queue: It is characterized by the maximum permissible number
of units that it can contain. Queues may be infinite or finite.
- Service Discipline: It refers to the order in which members
of the queue are selected for service. Frequently, the discipline
is first come, first served.
Following are some other disciplines:
- LIFO (Last In First Out)
- SIRO (Service In Random Order)
- Priority System
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"FIFO is the easiest
ordering to handle in mathematical models." - Vinay Chhabra
& Manish Dewan |
- Service Mechanism: A specification of the service mechanism
includes a description of time to complete a service and the number
of customers who are satisfied at each service event. The service
mechanism also prescribes the number and configuration of servers.
If there is more than one service facility, the calling unit may receive
service from a sequence of these. At a given facility, the unit enters
one of the parallel service channels and is completely serviced by
that server. Most elementary models assume one service facility with
either one or a finite number of servers.The following figure shows
the physical layout of service facilities.
Unusual Customer/Server Behaviour
Customer's Behaviour
- Balking. A customer may not like to join the queue due to
long waiting line.
- Reneging. A customer may leave the queue after waiting for
sometime due to impatience.
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"My patience is now at
an end." - Hitler |
- Collusion. Several customers may cooperate and only one of
them may stand in the queue.
- Jockeying. When there are a number of queues, a customer
may move from one queue to another in hope of receiving the service
quickly.
Server's Behaviour
- Failure. The service may be interrupted due to failure of
a server (machinery).
- Changing service rates. A server may speed up or slow down,
depending on the number of customers in the queue. For example, when
the queue is long, a server may speed up in response to the pressure.
On the contrary, it may slow down if the queue is very small.
- Batch processing. A server may service several customers
simultaneously, a phenomenon known as batch processing.
 
- The source population has infinite size.
- The inter-arrival time has an exponential probability distribution
with a mean arrival rate of l customer arrivals per unit time.
- There is no unusual customer behaviour.
- The service discipline is FIFO.
- The service time has an exponential probability distribution with
a mean service rate of m service completions per unit time.
- The mean arrival rate is less than the mean service rate, i.e.,
l < m.
- There is no unusual server behaviour.
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