### Analysis Of Length Of Busy Periods Of Dual Data Traffic Using Queueing System Abstract

Analysis Of Length Of Busy Periods Of Dual Data Traffic Using Queueing System

Abstract:

The Queueing theory is used in this paper to model the dual data traffic. Analysis of length of busy period of dual data traffic of any communication system using queueing theory approach, gives over all information about internal system behavior when system is either busy or Idle. Morkov chain is developed to analyze the system busy period and the system utilization is also analyzed and the length of the busy period is also analyzed .

Introduction:

Due to increasing trends of in the field of communication system of various data types, it is hard to analyze the various data types. In continuous time system the data is analyzed through the equations which shows the system behavior but through equations it is difficult to understand the over all internal behavior of the system. The queueing theory provides the theoretical framework of the system design and provide the internal behavior of the system. It is the mathematical study of busy periods and idle periods. Queueing theory enables mathematical equations for analysis of different simillar processes, including arriving at the queue, busy periods, waiting in the queue and being served at the front of the queue. Using this theory we measure the busy period, length of busy period time in the queue or the system, the expected number waiting or receiving service and the probability of encountering the system.

Markov processes provide better, powerful means for description and analysis of internal system properties. When a system is modeled by an irreducible continuous time Markov chain(CTMC), there is often an interest in computing a steady state measure which can be expressed as a linear function of the steady state probability distribution of the whole system. the morkov chain provides the full internal operation of the system. The Morkov chain is constructed through the queuing system which shows the over all information of the system behavior. The length of the busy period is analyzed with the Morkov chain and the busy period is also analyzed and the total system utilization.

Methodology

Construction of Queuing system of dual data traffic flow.

Most real-life queueing systems have more than one service facility. The output of one facility may proceed to another facility for further processing, or return to a facility already visited for rework or additional work of a different type. Examples abound: assembly lines, ?ow shops, and job shops in manufacturing, traf?c ?ow in a network of highways, processing in order-ful?llment systems, client server computer systems, telecommunications networks— both POTS (“plain old telephone service) and the emerging high-speed packet-switched networks designed to carry avariety of services, including data transfers, conferencing, web browsing, and streaming audio-video. Early in the postwar period, several researchers in queueing theory turned their attention to networks of queues, recognizing the importance of the applications. Queueing system is a model which contains the following structure as the customers arrive and join a queue to wait for the service provided by n servers. After receiving the service, the customer exits the system. As the Queueing Strategies are as follows : * FIFO(First in First Out) – customers are serviced according to their order of arrival in the queue. * LIFO(Last in First Out) – the last customer to arrive on the queue is the one who is serviced first. * PS(Processor Sharing) – customers are serviced equally. * SIRO (service in random order)- customers are serviced in a random order. * PR (priority) – customers are serviced based on the priority.

The morkov system consist of two queue or more than two queue (depending on the number of arrivals), the queue1 given the name by ?1 (lamda) and the queue2 given the name ?2 (lamda) in which dual data type arrives. Both queue served by single server/casher with exponential distribution (µ).

Fig. 1. Queueing System

Morkov chain of the system.

The system morkov chain of dual data type is shown in above fig. the system consists of two variables i and j ,the above one represent the function of queue1 having the single class customers and the arrivals rate is represented by ?1 while the second second class customers are represented by the below one with arrival rate of ?2.

When the system is empity the system condition is (0,0) in the morkov chain system whenever any arrival occurs in the system either in queue1 or in queue2 the system condition becomes (1,0) or (0,1) when any one of the system reaches at maximum level capacity the system becomes (3,0) or (0,3) and the (3,3) system condition represent the maximum capacity level of the system.

Fig. 2. Markov chain

To summarize at lest two inputs are needed to define a queue1 and queue2 with arrival rate of ?1 and ?2 with server(µ).

Depending on the situation may need other inputs describing the extent of variability in arrival and server . we assumed certain type of variability of (poisson distribution for number of arrivals and exponential distribution for service time).

Busy period Morkov chain.

The morkov chain busy period fig shown below is constructed from the system morkov chain the busy period of the morkov chain is consist of those states of the morkov chain when the system is busy the calculation of length of busy period starts when the system is idle and customers are arrives in the system.

Fig. 3. Markov chain of busy period

Busy period analysis.

Analytical analysis.

Aims or objectives

To analyze the system busy period.

To analyze the length of busy period

To analyze the system utilization

Conclusion

References