Performance Evaluation of Modified Phase Type Communication Network with Load Dependent Transmission

Abstract

Recently much emphasis has been given for performance evaluation of communication networks with different transmission policies. Suresh Varma and Srinivasa Rao (2005) have developed a communication network with load dependent transmission applying tandem queuing model. However, in some places like internet communication, Broadband networks, satellite communication, computer communication etc., the transmission rate depends on the load of the connected buffer and some jobs (packets) are terminated immediately after the first transmitter, the remaining packets are to be transformed through the second transmitter i.e. the transmission of packets takes place in each of the several successive transmitters. At each transmitter the packet has an option either to leave the network or enter the subsequent buffer. This type of the transmission is called modified phase type transmission. In this paper we develop and analyze a communication network with load dependent having modified phase type transmission. The network is approximated with the Poisson processes through statistical multiplexing. The transient analysis of the network is carried out by studying the congestion in the buffer and delays in transmission. It is observed that load dependence has tremendous influence on congestion control.

Multi Node Tandem Queuing Model with Binomial Bulk Size Distribution Having Load Dependent Service

“…Putting in (11) we get the probability generating function of i th queue size distribution = (21) Mean number of customers in i th queue is (22) Where E( is the mean of batch size arrivals to first queue and is given by Putting in (21)we get the probability that the i th queue is empty as (23) Utilization of i th server is (24) Throughput of i th server is (25) Average waiting time of a customer in i th queue is = (26) Variance of the number of customers in i th queue is = (27) Coefficient of variation of the number of customers in i th queue is (28)…”

Stochastic control of K-parallel and series queuing model and its applications

“…Recently, much work has been focused on load dependent queueing models. Choi and Choi (1996), Parthasarathy and Selvaraju (2001), Leung (2002), Suresh Varma and Srinivasa Rao (2007), Padmavathi et al (2009), Trinatha Rao et al (2012 and others have developed queueing models with load dependent service rates. In all these papers they assumed that the systems are in single and arrivals are characterized by Poisson processes.…”

Multi Node Tandem Queuing Model with Bulk Arrivals Having Geometric Arrival Distribution

“…In order to streamline the bulk arrivals, forked queuing models are proposed. [11][12][13][14][15][16][17], [44], [45].The customers arrived at a service point (first node) are diverted to (K-1) nodes for various services .The models are developed and studied with various distribution processes (Uniform, Poisson, Geometric, Binomial etc.,)to closely represent the real time situation. To further simplify the service activity and to establish direct relation between the first node and the secondary nodes tandem queuing models are designed.…”

“…In a Tandem queuing model , the output of first queue formulates the input for the other. These models could be load dependent (situations where service time is adjusted w.r.t .the number of customers) [11][12][13][14][15][16][17] , [22], [23], [44][45]or load independent [17], [8], [10], [4], [36]. In recent work [18] , the present authors studied a multi node tandem queuing model with load dependent service rates.…”