International Journal of Computer Networking, Wireless and Mobile Communications (IJCNWMC) ISSN 2250-1568 Vol. 3 Issue 2, Jun 2013, 83-92 © TJPRC Pvt. Ltd. INFLUENCE OF G.P ON NETWORKS - A SCIENTIFIC STUDY ON CASE (I) K. V. L. N. ACHARYULU 1 & NAGU VADLANA 2 1 Faculty of Mathematics, Department of Mathematics, Bapatla Engineering College, Bapatla, India 2 Faculty of Computer Science, Department of MCA, Bapatla Engineering College, Bapatla, India ABSTRACT The Paper deals with the investigation on Geometric Progression (G.P) which explains whether it will indorse the network or not in a special case of Network.The large scale network is illustrated in a taxonomical way with 94 nodes and 124 activities. G.P is conceived on a most likely time estimate among the three time estimates namely optimistic, most likely and pessimistic. Scientific study has been accomplished on the considered network. Some remarkable results are found. All float values are also computed. Critical path is identified and project analysis has been fulfilled. Periodical analysis is instituted with standard normal distribution curves which are depicted wherever necessary. KEYWORDS: Network, Time Estimates, Float, Critical Path, Normal Distribution AMS Classification: 90-08, 90B10, 90C90 INRTRODUCTION A large scale project needs three phases to complete it successfully .The quantity of Planning,scheduling and controlling will provide the best path to reach the required goals in any Project.PERT is the effective and efficient tool to run the large scale projects with expediting the process and controlling the utilization of available resources.PERT was initiated between 1958 and 1959 as a research idea for the development of U.S Navy Polaris Missile Program.PERT algorithm has been utilized in many sectors in a number of areas of computer and non computer industries since 1959. PERT is most applicable algorithm to huge projects even though they have high degrees of uncertainty. Levin and Kirkpatrick [5] discussed about planning and control of a project with the aid of PERT and CPM in 1966.Wiest and Levy [6] investigated new ideas on Networks with management guide to PERT/CPM for research scholars in the area of operations research. Billy E.Gillett [7] explained different models of operations Research in 1979. S.D Sharma [8] studied the application area of PERT&CPM techniques.K.V.L.N.Acharyulu et.al [1-4] examined some peculiar cases of Game theory problems. The authors in this paper studied to identify whether Geometric progression in a special case will affirm a network or not. The Geometric progression is applied on most likely time estimate among the three time estimations. By the concept of Mathematical induction, few results are obtained. Project analysis is also carried out. Total Float, Free float and Independent Float are calculated inview of getting critical path. The standard normal distribution curves are drawn with the aid of Mat lab wherever necessary. CONSTRUCTION OF NETWORK A network is drawn with 94 nodes and 124 activities in a step by step way for investigating the effect of Geometric Progression. G.P is employed on most likely time estimate (m) in case (I) among the three estimates. Network does not allow any error and dummy activity.