Vol-08 Issue 11, November -2024 ISSN: 2456-9348 Impact Factor: 7.936 International Journal of Engineering Technology Research & Management Published By: https://www.ijetrm.com/ IJETRM (http://ijetrm.com/) [30] SHORTEST PATH IN STOCHASTIC COMMUNICATION NETWOKS Dr. M. Maruthi Rao 1 , N.V. Surya Narayana 2 S. Praveena 3 , S.Lakshmi 4 , P.Indraprasta 5 , 1 Associate Professor, Dept; of ME, AITS (Autonomous), Tirupati, AP, India 2 Assistant Professor, Dept; of ME, PBR VITS (Autonomous), Kavali, AP, India. 3,4,5 Assistant Professor, Dept; of ME, AITS (Autonomous), Tirupati, AP, India ABSTRACT The project presents a Methodology to compute shortest path in a stochastic communication network. In this stochastic communication network shortest path from source node to sink node is calculated by considering all possible paths, in which all nodes are capable of source node to sink node is calculated by considering all possible paths, in which all nodes are capable of receiving and transmitting messages. Here the messages are assumed to be travel between the pair of nodes with specified speed which varies for different pairs of nodes and the travel times between the nodes are allowed to be an exponentially distributed random variables. The problem is formulated as a chance constrained programming in stochastic communication network with the objective of minimizing the distance between the source and sink nodes. The results of the proposed methodology for this stochastic communication network under consideration are documented and compared with that of an existing methodology. Keywords: Shortest path, Maximize, Minimize, Net work, Nodes. INTRODUCTION A sub graph of a graph (G) with N - 1 links that has no circuits is called a spanning tree of G with N nodes. It has been extensively researched to generate all spanning trees of G without flow. For instance, 1–5. The system resilience of a computer network has been determined using these spanning trees without flow (6 –8). A proposed spanning tree with flow9 employs an algorithm that consists of two main steps: To determine the spanning trees with flow, first create spanning trees without flow using the Cartesian product of all pathways. PROPOSED METHODOLOGY Consider a Communication Network G (n, a) with nodes (n) as stations capable of receiving and transmitting messages and arcs (a) as one why communication links connecting the pairs of nodes. The messages are assumed to be travel between the pairs of nodes (i, j) with specified speed, which varies for different pairs of nodes, and the messages transmitting time t, to node j from i is Random Variable. In order to compute expected length from source node to sink node The problem can be formulated as a chance constrained programming problem as follows. Minimize Z = Subject to P { ≤ lm} ≥( I – αm) i.e., Σ Σ tij xij < lm is realized with a minimum probability of (1-αm) i j Where lm is Maximum allowable path length m1,2,3……N 0<αm<1 Here the separable convex programming technique is used to solve this approximate model. Now consider the separable functions as follows. ( ) =