THREE NODE TANDEM COMMUNICATION NETWORK MODEL WITH DUANE ARRIVALS AND DYNAMIC BANDWIDTH ALLOCATION K. Srinivasa Rao Department of Statistics Andhra University Visakhapatnam India ksraoau@yahoo.co.in Kalavala AsishVardhan Department of CS&SE Andhra University Visakhapatnam India ashi.mintu@gmail.com P. Srinivasa Rao Department of CS&SE Andhra University Visakhapatnam India peri.srinivasarao@yahoo.com ABSTRACT: Conducting the laboratory experiments is time consuming and complicated. The mathematical models for the innovative communication networks is a prerequisite for designing and analyzing the communication networks. In Communication Systems such as Telecommunications, Satellite Communications, Computer Communications, the arrival of packets to the buffers are time dependent and bursty. This paper addresses a three node communication network model with time dependent arrivals having dynamic band width allocation. The time dependent arrivals are characterized by Duane process. It is further assumed that the inter transmission times in all nodes follow Exponential distribution. The joint probability of the number of packets in each buffer is derived. The explicit expressions for the system characteristics are obtained. The Sensitivity analysis of the model revealed that the time dependent arrival process can predict the performance measures more close to the reality. The DBA strategy can reduce the conjunction in buffer and avoid burstness. This model can also include some of the earlier model as particular cases. Keywords: Duane Process, Three node Tandem Communication networks, Performance Evaluation, Sensitivity Analysis. 1. INTRODUCTION Recently, much work has been reported in literature regarding, modeling the communication networks / data voice transmission with various assumptions. In these models, it is customary to assume that packets or connection arrivals follow Poisson process because such process is simple and much theory is available with attractive properties (V. Frost and B. Melamed, (1994)). This is also supported by Abry et al (2002), Cappe et al (2002). Who stated that the Poisson like nature show that aggregate traffic smoother or less bursty. But the studies made by Jain and Routhier (1986), Gusella et al (1990), Fowler and Leland (1991), Danzig, Jamin, Caceres, Mitzel, and Estrin (1992) revealed that in the Local Area Network (LAN), Wide Area Network (WAN) and Metropolitan Area Network (MAN) traffic the packet arrival distribution is not exponential. Similarly, Leland, et al (1994), have studied the LAN traffic can be better modeled by self-similar processes which differ significantly from Poisson Process. In these networks the traffic burst appears over a wide range of time scales. Vern Paxson and Floyd (1995) have pointed that the Poisson Process, fails in modeling the WAN traffic, because of time dependent nature of the arrivals. Recently, much emphasis is given for modeling the arrival process of the communication networks using, Nonhomogeneous Poisson Process with the assumption that the arrival rate is linearly dependent on time (M. V. Rama Sundari, K. Srinivasa Rao, P. Srinivasa Rao, P. Suresh Varma (2011), Trinatha Rao. P et al (2012), Suhasini, A. V. S. et al (2013a), Suhasini, A. V. S. et al (2013b)). In all these papers they assumed that the burstness of the traffic is either linearly dependent on time. But in LAN, WAN, and MAN the traffic structure is quite different from the, arrival rates being linearly dependent function of time. This is also supported by Rakesh Singhai et al (2007) who have, modeled the packet arrivals as Log Normal distributions, since, the associated network traffic inter arrivals are distributed with heavy tail distributions. Feldmann (2000) demonstrated that the Transport Control Protocol International Journal of Computer Science and Information Security (IJCSIS), Vol. 16, No. 12, December 2018 54 https://sites.google.com/site/ijcsis/ ISSN 1947-5500