Page 115 - DCAP601_SIMULATION_AND_MODELING

Unit 7: Simulation of Queuing System (I)

Under the caption of “Characteristics of a Waiting-Line System”, they spell out Arrival, Waiting- Notes
Line, and Service Facility in a pattern analogous to what has been specified above. Now I will
describe four specific models as valuable POM applications:
1. Single Channel Queuing Model: which includes a single Queue and a single Service Facility
and presumes that Arrivals are limitless and can be officially treated in a Poisson
Distribution. Service Times are understood to take on the form of an Exponential
Distribution (reflecting the normal uncertainty of service times).
2. Multiple-Channel Queuing Model: which adds a 2nd Queue intended for a 2nd Service
Facility.
3. Constant Service Time Model: This shows a single Queue leading to a single Service
Facility which, in turn, handles each consumer in the precise same quantity of time. Here
the Exponential Distribution does not relate to Service Time.
4. Limited Population Model - which concerns with a inadequate number of Arrivals and a
single server and relates to circumstances where a single operator (the Service Facility)
deals with a restricted number of machines (the Queue).
We have seen that as a system gets congested, the service delay in the system increases. A good
perceptive of the relationship between congestion and delay is essential for designing effective
congestion control algorithms. Queuing Theory provides all the tools needed for this analysis.
This article will focus on understanding the basics of this topic.

Communication Delays

Before we proceed further, lets understand the diverse components of delay in a messaging
system. The total delay experienced by messages can be classified into the following categories:

Processing Delay  This is the delay between the time of receipt of a packet for
transmission to the point of putting it into the transmission
queue.
 On the receive end, it is the delay between the time of reception
of a packet in the receive queue to the point of actual processing
of the message.
 This delay depends on the CPU speed and CPU load in the
system.
Queuing Delay  This is the delay between the point of entry of a packet in the
transmit queue to the actual point of transmission of the
message.
 This delay depends on the load on the communication link.
Transmission Delay  This is the delay between the transmission of first bit of the
packet to the transmission of the last bit.
 This delay depends on the speed of the communication link.
Propagation Delay  This is the delay between the point of transmission of the last bit
of the packet to the point of reception of last bit of the packet at
the other end.
 This delay depends on the physical characteristics of the
communication link.
Retransmission Delay  This is the delay that results when a packet is lost and has to be
retransmitted.
 This delay depends on the error rate on the link and the protocol
used for retransmissions.

In this article we will be dealing primarily with queueing delay.

LOVELY PROFESSIONAL UNIVERSITY 109