14-02-2013, 03:58 PM
Queueing Theory
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Introduction
•A key feature of communication networks is the sharing of resources such as transmission bandwidth, storage and processing capacity.
•Since the demand for these resources is unscheduled, the situation can arise where resources are not available when a user places a request.
•This situation leads to a delay or loss in service.
•One of the most important performance measures of a data network is the average delay required to deliver a packet from origin to destination.
•Delay considerations strongly influence the choice and performance of network algorithms such as routing and flow control.
•Hence it is important to understand the nature and mechanism of delay and the manner in which it depends on the characteristics of the network.
•Queueing theory is the primary methodological framework for analysing network delay.
•Its use often requires simplifying realsistic assumptions which make meaningful analysis extremely difficult. Hence sometimes it is impossible to obtain accurate quantitative delay predictions on the basis of queueing models.
•Present study discusses about Packet delay within the communication subnet (ie. Network layer). This delay is the sum of delays on each subnet link traversed by the packet.
Multiplexing of traffic on a communication Link
•Commonly used scheme is statistical multiplexing where the packets of all traffic streams are merged into a single queue and transmitted on a first come first serve basis.
•A variation of this scheme is used which maintains separate queue for each traffic stream and serves the queues in sequence one packet at a time.
•Since the entire transmission capacity(Cbits/sec) is allocated to a single packet(Lbits long), it takes L/C secs to transmit a packet.
Queueing Models
•Consider queueing systems where packets arrive at random times to a communication link for transmission in a data network.
•Service time corresponds to the packet transmission time and is given as L/C.
•It is also assumed that packet lengths include frame header and trailer.
•Customers represent ongoing conversations and service time corresponds to duration of a conversation.
•Following quantities are estimated:
1.Average number of customers.
2.Average delay per customer.
•These customers are estimated using-
1.Customer arrival rate
2.Customer service