Analytic solutions of a stochastic banking model with upper truncated amount of withdrawals

Stochastic Banking models (S.B.Ms) occupy an important place in modern research, dealing with cash flow analysis of a Banking System. Knowledge about the reserve level of a Banking system, play a vital role in many Fiscal policies of any economy. To have prospective and fruitful economic plans, one must have a prior knowledge about the cash reserve level available with the nation, without which the plans will be vague and ineffective. Hence in 1983 [3] proposed a stochastic banking model (S.B.M) with a critical reserve level (C ≥ 0) and obtain many results relating to the reserve level X(t) available with the system at any given time t ≥ 0, (vide Ref.2). Later in 1991, Sarma and Pushpanjali [5] Proposed a S.B.M.with general linear rate of inputs and obtained explicit expressions of M/G/1/FIFO/K and G/M/1/FIFO/K S.B.Ms. Further in 1995, Sarma and Sarma [6] obtained results of S.B.Ms where withdrawals or inter – withdrawals are assume to follow an Erlangian distribution. The application of this distribution to S.B.M.has more practical relevance because the service of a customer in a Bank consists of different phases like issuing of tokens, passing of the amount, making suitable entries and so on.

Thus more and more practically relevant assumptions were brought in to the model, so that the S.B.M. suggested in 1983 is more and more closer to the reality.

In this paper a practically valid and more essential assumption namely “Upper Truncation of Amount of Withdrawals” is incorporated into the Stochastic Banking Model in order to make the model more closer to reality and to increase the application potentiality of the model. An analytic solution of a M/M^a/1/FIFO/∞ Stochastic Banking Model (S.B.M) is obtained, Where M^a represents a upper truncated Law governing the random variable of amount of withdrawals.