Page 103 - DCAP601_SIMULATION_AND_MODELING

Unit 7: Simulation of Queuing System (I)

7.1 Simulation of Queuing System Notes

General Queue

In a queuing system, the calling population is assumed to be infinite that is, if a unit leaves the
calling population and joins the waiting line or enters service; there is no change in the arrival
rate. Figure 7.1 shows the model used to analyze a general queue.
The arrivals occur one at a time in a random order and once the customer joins the queuing
system he will eventually receive the service.

Figure 7.1: A Simple Queue

The arrival rate and services are modeled as variables which follow statistical distributions. If
the arrival rate is greater than the service rate, the waiting line will grow without bound.

Did u know? Arrival pattern
The arrival pattern of consumers to the service system is categorized into two groups:
static and dynamic. These two are further classified depending on the nature of arrival rate
and the control that can be work out on the arrival pattern.
In static arrival process, the control is based on the nature of arrival rate (random or
stable). Random arrivals are either at a stable rate or unstable with time. Therefore to
examine the queuing system, it is essential to endeavor to portray the possibility
distribution of arrivals.
The dynamic arrival process is restricted by both service facility and consumers. The
service facility regulates its capacity to match alterations in the demand intensity, by
either changing the staffing levels at dissimilar timings of service, modifying service
charges (like telephone call charges at unusual hours of the day or week) at unusual
timings, or permitting entry with schedules.

7.1.1 Single-channel Queuing System

The single-channel queuing system can be seen in places such as banks and post offices, where
one single queue will diverge into a few counters. The moment a customer leaves a service
station, the customer at the head of the queue will go to the server. The disadvantage of a single-
channel queue is that the queue length seems to be very long, thus it can discourage customers
from joining the queue.

LOVELY PROFESSIONAL UNIVERSITY 97