Blocking and Delays in M (x) /M/c Bulk Arrival Queueing Systems

This paper presents results for queueing systems that are characterized by poisson arrival epochs with x (a random variable) arrivals at each epoch, exponential service times and c servers. The steady state probabilities, the probability of blocking (not being served immediately) for both loss and delay systems are investigated. In addition, the average delay, the variance of the delay and the delay distribution for first-come-served by batches and arbitrary order of service within batches are presented.

Random Variables, the Time Value of Money and Capital Expenditures

This paper treats the following problem. How much money should be invested at time t 0 at an interest rate of I for a time T such that the probability of the funds required "K(T)" exceeding those available "X(T)" equals at most p. That is P{K(T) > X(T)} 0 ) exp{ I(T - t 0)}. The parameters I, T, X(T) and K(T) are taken to be random variables. The theory to solve the stated problem is presented and solutions to certain specific cases are given.