Toshiharu Hasegawa

An Approximation Method for Open Restricted Queueing Networks

This paper presents an approximation method for analyzing open restricted queueing networks with exponential service time and Poisson arrivals. Analysis is made by node-by-node decomposition through the introduction of a pseudo-arrival rate and an effective service rate. The method is applied to example networks and evaluated by comparing the results obtained thereby with those by simulations or exact calculations. We find that this method provides a fairly good approximation procedure for obtaining system performance measures such as blocking probabilities, output rates, etc., in open restricted queueing networks.

An analysis of a discrete-time queue for broadband ISDN with priorities among traffic classes

In broadband ISDN, different classes of traffic expect to receive different quality of service. One way of providing service is to implement a priority structure among traffic classes. The authors analyze a single server queue in which video and voice traffic receive priority over data traffic. Corresponding to the fixed cell size of ATM, they assume that service times are deterministic. They further assume that the high priority traffic is correlated and the arrivals are governed by a Markov chain. With these assumptions, they characterize the queue length distributions and the waiting time distributions for this problem. They show by numerical examples that the delay distribution depends highly on the correlations and that a priority service discipline is capable of providing very good service for real time traffic. >

Cell loss and output process analyses of a finite-buffer discrete-time ATM queueing system with correlated arrivals

The performance of an asynchronous transfer mode (ATM) switching node is analyzed, taking cell arrival correlation into consideration. An ATM switching node is modeled as a discrete-time finite-buffer queue. Cell arrivals are assumed to follow a semi Markovian process. Various characteristics of the cell loss and the distribution function of the cell output process from an ATM switching node are analyzed. The cell loss probability, the consecutive loss probability, the distribution of loss period lengths, the joint distribution of successive cell interdeparture times, and the distributions of busy and idle periods are determined. It is shown that both the correlation and the variation of cell arrivals significantly affect the cell loss and the output process characteristics.<<ETX>>

Exact analysis of asymmetric polling systems with single buffers

A unified approach to general asymmetric polling systems with a single buffer at each station is presented. Two variations of single-buffer polling system are considered: the conventional system and the buffer-relaxation system. In the conventional system, a new massage is not allowed to queue until the previous message has been completely transmitted, while in the buffer-relaxation system, a newly arriving message can be stored in the buffer once the previous messages transmission has started. For each system, the Laplace-Stieltjies transform (LST) of the joint probability-distribution function (PDF) of station times is derived, from which the LST of the PDF of message delay is straightforwardly obtained. >

Mean waiting times in nonpreemptive priority queues with Markovian arrival and i.i.d. service processes

Abstract This paper considers nonpreemptive priority queues with P (>=2) classes of customers. Customers in each class arrive to the system according to a Markovian Arrival Process (MAP). MAP is a class of non-renewal arrival processes and includes the Markov Modulated Poisson Process (MMPP). The service times of customers in all classes are independent and identically distributed according to a common distribution function. Using both generating function techniques and matrix analytic methods, we derive the mean waiting time for each customer class. The algorithmic implementation of the analytical results is also discussed along with numerical examples.

Analysis of a nonpreemptive priority queue with SPP arrivals of high class

Abstract This paper considers a nonpreemptive priority queueing system with two priority classes of customers, where high priority customers arrive to the system in accordance with a switched Poisson process ( SPP ) and low priority customers in accordance with a Poisson process. Using the supplementary variable technique, we derive the joint probability generating function of the stationary queue length distributions and the Laplace-Stieltjes transforms of the stationary waiting time distributions of high and low priority customers. We also present some numerical results in order to show the computational feasibility of the analytical results.

Performance Analysis of a Polling System with Single Buffers and Its Application to Interconnected Networks

We first consider the interdeparture process of a symmetric polling system with single buffer at each station, where distributions of transmission time and switchover time are assumed to be general. Under the assumption that consecutive interdeparture times are independent, the probability distribution is analyzed and the LaplaceStieltjes transform is given. Numerical examples show that the coefficient of variation of interdeparture time is not monotonic with respect to the arrival rate. Based upon the analysis, we can obtain the characteristics of outbound traffic if we are concerned with unidirectional traffic flow. In general, however, there is inbound traffic from external networks in the interconnected communication system and its effect on performance characteristics should be taken into account. We next propose the model of a polling system having the traffic from outside the system. The model consists of homogeneous stations with single buffers and a depot station with infinite buffer where inbound traffic is dealt with. We analyze the model and obtain throughput and mean waiting time for the case of constant transmission time and constant switchover times. Numerical examples show that the throughput of the system is not sensitive to inbound traffic if the total load of the system is moderate.

Waiting time and queue length distributions for go-back-N and selective-repeat ARQ protocols

The paper provides a performance analysis of automatic-repeat-request (ARQ) protocols in connection-oriented transmission. Each message arriving at a transmitter is divided into several packets, which are continuously transmitted to a receiver according to go-back-N ARQ or selective-repeat ARQ protocols. Because of connection-oriented transmission, messages are served on a first come first served basis, i.e., transmission of a message is commenced after all packets in the previous message are successfully transmitted. For the two ARQ protocols, the authors derive the probability generating functions of message waiting time and queue length at an arbitrary instant, from which the average performance measures are explicitly obtained. >

Fundamental algorithm for train scheduling based on artificial intelligence

The trial-and-error efforts by experts have been considered as indispensable in compiling railroad timetables. There is a strong requirement to computerize the procedure, but it has been considered difficult. It is proposed to merge the following two concepts as a means to obtain an efficient trial-and-error procedure, which is the basis of the compilation of railroad timetables: (1) the concept of (time) belt, where a number of alternatives for arrival and departure is handled as one alternative, considering only the order of arrivals and departures; (2) the concept of the propagation of constraints, which is well known in the artificial intelligence where alternatives in conflict to the order of arrivals and departures are eliminated. This paper discusses the scheduling problem for the partially ordered set of events. The requirement for the time difference between events is considered as a constraint. An algorithm is proposed which calculates the permissible range of time for the event generation, as a closed interval on the time axis. It is shown that the constructed algorithm can be applied as the basic algorithm for the railroad timetable compilation system, where the timetable is considered as a specification for the order of arrivals and departures of the trains, and the arrival-departure time is considered as a belt. An efficient method of compilating the timetable by the proposed algorithm is presented, based on the search for the possible orders of the trains, together with the construction example of the timetable for the actual railway.

Performance Evaluation of an Integrated Access Scheme in a Satellite Communication Channel

A method for realizing a circuit and packet integrated access scheme in a satellite communication channel is considered. Two kinds of terminals are assumed, namely, bursty terminals for handling bursty traffic and heavily loaded terminals for long-holdingtime message traffic. In this method, the channel frame is divided into two subframes: one is for bursty terminals, and the other is for heavily loaded terminals. The subframe for heavily loaded terminals is further divided into two subchannels, a reservation subchannel (consisting of small slots) and a message subchannel. The bursty terminals transmit their packets in their dedicated subframes on the slotted ALOHA protocol. The heavily loaded terminal having a message transmits, first of all, a reservation packet in a randomly selected small slot of the reservation subchannel to reserve slots in the coming message subchannels. One slot in the same position of each of the succeeding message subchannels is reserved for the terminal until the end-of-use flag, transmitted from the terminal, is received by the satellite. Mean transmission delays for both kinds of traffic in this method are analytically obtained. We show that there exists an optimal frame length which minimizes mean transmission delay for one kind of traffic while keeping mean transmission delay for the other kind under some permissible value.