This paper deals with a single server serving N priority classes ( N being finite or infinite) and working under an FB z regime, namely, one in which the waiting line consists of infinitely many separate queues obeying the FIFO rule. Each priority class is assigned to one of the queues. A customer from the k th priority class (“ k -customer”) in the n th queue is eligible for θ n,k time units of service, at the end of which he either departs, because his requirement is satisfied, or joins the tail of the ( n + 1)-th queue. When a quantum of service is completed, the server turns to the first customer in the lowest index (highest priority) nonempty queue. The arrival process of k -customers is assumed to be homogeneous Poisson, and their service requirements are independent, generally distributed, random variable. A set of recursive linear equations is derived for the expected flow time of a k -customer whose service requirement is known, and some examples are discussed and presented graphically. This paper corrects some errors in an earlier paper by the second author.

This paper deals with a single-server station (a computer) where each customer's demand comprises an independent random number of jobs (programs). Under certain assumptions, two cyclic disciplines are mathematically analyzed: (a) continuous job service—a round-robin discipline where the quantum's length is distributed as the service requirement of a job; (b) intermittent job service—a double round-robin discipline—in the first instance in terms of the jobs within the customer's demand, and in the second in terms of the customer himself.

A simple computer system is described, which consists of a CPU and I/O unit and which works in a multiprogramming manner.The model assumes that the system works under heavy load so that the incoming queue is never empty, that the service times at the two units are exponentially distributed independent random variables, and that the number of iterations of the programs is geometrically distributed.Head of the line priority of programs which are being processed over newcomers is considered.Steady state distribution of the states of the system is numerically solved under the assumption of a finite waiting room.The suggested system is compared with one working in "batch mode" and with an equivalent multiprogramming system with a constant number of programs.The latter comparison shows that the suggested priority rule improves the expected response time without affecting the throughput and the utilizations of the CPU and the I/O unit.The model induces an interesting dependence phenomenon which is discussed at length.

This paper deals with a single server station delivering service to m priority classes (m might be finite or infinite).The arrival process of customers from a jth (j = 1, 2,..., m) priority class (jth customers) to a single server station is a homogenous Poisson process with rate X3 • Service requirements of jth customers are exponentially distributed with mean 1/~.The waiting line consists of infinitely many separate queues all of which obey the FIFO rule.Each priority class is assigned to one of the queues.A newly arrived jth customer joins the end of a predetermined queue.In the ith (i = 1, 2,...) queue a customer is eligible for a certain amount of service following which he either departs when his service requirement has been satisfied or joins the end of the (i + 1)th queue for additional service.When a quantum of service is completed, the server attends to the first customer in the lowest index (highest priority) nonempty queue.In such a priority regime, long and unknown in advance service requirements in all priority classes are dynamically penalized by degrading their priority degree.This paper derives mathematical expressions for calculating the expected total flow time of a jth customer whose service requirement is known.

This note deals with time-sharing disciplines where the arrival process is homogeneous Poisson and service requirements are exponentially distributed.The investigated regimes are: (A) ordinary round-robin (R.R.), (B) R.R. with the quantum allocated to a customer is a function of the number of quanta he has already received.These models were studied by Shemer, who derived for both models mathematical expressions for the expected total response time of a customer whose service requirement is given.Shemer's results are in disagreement with those of other authors and may only serve as a good approximation.His method is utilized here in a more general case of model (A) (with the discrepancies eliminated), and it also yields, after some improvement, a better approximation for model (B).

The paper deals with computer time-sharing disciplines in which external priorities are introduced. For a computer system under a time-sharing discipline, the following priority disciplines are discussed: (a) head-of-the-line; (b) preemptive repeat; and (c) mixed preemptive strategy. All models in question assume that customers arrive according to homogeneous Poisson processes, and that service times are mutually independent exponentially distributed random variables. Results are given in terms of steady-state expectations.

A time-sharing queue serving a finite number of customers is described. It is assumed that both the service time and the time elapsing between termination of service and the next arrival of the same customer at the queue (service station) are exponential. The model was studied by Krishnamoorthi and Wood, but their results are not in complete agreement with the results of this paper. In addition, some new results are presented in terms of steady-state expectations.