Page 222 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 11: Queuing Theory

1. The Arrival Pattern: The arrival pattern describes how a customer may become a part of Notes
the queuing system. The arrival time for any customer is unpredictable. Therefore, the
arrival time and the number of customers arriving at any specified time intervals are
usually random variables. A Poisson distribution of arrivals correspond to arrivals at
random. In Poisson distribution, successive customers arrive after intervals which
independently are and exponentially distributed. The Poisson distribution is important,
as it is a suitable mathematical model of many practical queuing systems as described by
the parameter “the average arrival rate”.
2. The Service Mechanism: The service mechanism is a description of resources required for
service. If there are infinite number of servers, then there will be no queue. If the number
of servers is finite, then the customers are served according to a specific order. The time
taken to serve a particular customer is called the service time. The service time is a statistical
variable and can be studied either as the number of services completed in a given period
of time or the completion period of a service.
3. The Queue Discipline: The most common queue discipline is the “First Come First Served”
(FCFS) or “First-in, First-out” (FIFO). Situations like waiting for a haircut, ticket-booking
counters follow FCFS discipline. Other disciplines include “Last In First Out” (LIFO)
where last customer is serviced first, “Service In Random Order” (SIRO) in which the
customers are serviced randomly irrespective of their arrivals. “Priority service” is when
the customers are grouped in priority classes based on urgency. “Preemptive Priority” is
the highest priority given to the customer who enters into the service, immediately, even
if a customer with lower priority is in service. “Non-preemptive priority” is where the
customer goes ahead in the queue, but will be served only after the completion of the
current service.
4. The Number of Customers Allowed in the System: Some of the queuing processes allow the
limitation to the capacity or size of the waiting room, so that the waiting line reaches a
certain length, no additional customers is allowed to enter until space becomes available
by a service completion. This type of situation means that there is a finite limit to the
maximum queue size.
5. The Number of Service Channels: The more the number of service channels in the service
facility, the greater the overall service rate of the facility. The combination of arrival rate
and service rate is critical for determining the number of service channels. When there are
a number of service channels available for service, then the arrangement of service depends
upon the design of the system’s service mechanism.
Parallel channels means, a number of channels providing identical service facilities so that
several customers may be served simultaneously. Series channel means a customer go through
successive ordered channels before service is completed. The arrangements of service facilities
are illustrated in Figure 11.2. A queuing system is called a one-server model, i.e., when the
system has only one server, and a multi-server model i.e., when the system has a number of
parallel channels, each with one server.

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