EVALUATION OF PROBABILITY MASS FUNCTION OF STARTING STATES OF FLOW PROCESS OF HYPOGEOMETRICAL EARLY ARRIVAL DISCRETE-TIME DSR LOAD MANAGEMENT SYSTEM

W. SHAH, S. A. A. SHAH, U. A. RIND

Abstract


Flow process is very effective technique to trace the flow path and time of customer when it arrives in the system. In this paper, we develop and evaluate the dual service rate load management system through hypogeometrical early arrival discrete time system. The flow process Markov chain of the system is constructed through system state and service process Markov chains which depicts the all flow paths and time of customer which can be entered at any starting state till the customer leave the system. The arrival process of the system is modeled by a two phase discrete time hypogeometrical distribution and service process is depends on the system size. We compute the starting states probability mass functions and total probability mass function to show the flow time of customer. For numerous values of arrival and service probabilities, analytical results obtained and they are validated through simulation results.


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