A hospital accepts k different types of patients, where type i patients arrive according to a Poisson proccess with rate λi , with these k Poisson processes being independent. Type i patients spend an exponentially distributed length of time with rate μi in the hospital, i = 1,..., k. Suppose that each type i patient in the hospital requires wi units of resources, and that the hospital will not accept a new patient if it would result in the total of all patient’s resource needs exceeding the amount C. Consequently, it is possible to have n1 type 1 patients, n2 type 2 patients,..., and nk type k patients in the hospital at the same time if and only if k

i=1 niwi C