In a personal communication system (PCS), a scheme for reforwarding call-terminating setup messages (SETUP messages) from a network or a cell station is used to guard against their loss. We have developed a method for evaluating the loss probability of a reforwarding scheme in which the network monitors the response messages from a personal station after forwarding a SETUP message to that personal station and reforwards the SETUP message only if a response message is not received. We started with a stochastic model in which messages registered in the paging-channel queue in a cell station are cyclically forwarded to the wireless area. This model corresponds to the finite-capacity M/D/1/N model with vacation time. We then added a method for calculating the "timeout" probability. Next we expanded the model into one in which the SETUP messages are reforwarded when a response message is not received by the network. This model corresponds to the M/D/1/N model with vacation time and retrials. We then added an approximate method for calculating the loss probability. Finally, using the proposed methods, we clarified the traffic characteristics of PCS call-terminating control.

The paper deals with a single server queue with two priority classes of customers. The arrival process for the high-priority class is assumed to be Poisson, while the interarrival time for the low-priority class is allowed to have a general distribution. Work-conserving rules, especially the non-preemptive rule and the preemptive-resume rule, are studied. A relationship between the unfinished work and the waiting times for both priority classes is derived. Numerical calculation for the unfinished work is not so easy, because the queueing model considered here contains the GI/G/1 model. Using a diffusion approximation for the unfinished work process, new approximate formulas for the performance measures are obtained explicitly. If the arrival process for the low-priority class is also Poisson, the formulas are consistent with the classical exact results. Numerical examples and comparisons with simulation results are presented. They indicate that the approximate formulas proposed here are accurate as compared with those presented in the previous works.

This paper presents queueing analysis methods for mixed loss and delay systems. The queueing models considered here are an extension of the previously analyzed models and are applicable to the Facsimile Intelligent Communication System (FICS). First, assuming compound Poisson arrivals and a single server, an exact result for performance measures of the model is obtained by the supplementary variable technique. Second, assuming general batch arrivals and many servers, a diffusion process approximation with the elementary return boundary is developed. A new recursive scheme for the steady-state distribution of the number of customers in the system is derived. Some numerical examples are provided and compared with exact and simulated results, which demonstrate the accuracy of the approximation.

The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewal-input GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.

We consider a finite-capacity single-server queue with constant service and vacation times, which is seen in the time division multiple access (TDMA) scheme. First we derive the probability that j customers remain in the queue when a test customer arrives. Using this probability we then evaluate the probability that the test customer who arrives during the vacation or service time has to wait in the queue for longer than a given time. From these results, we obtain the waiting time distribution for the customer arriving at an arbitrary time. We also show a practical application to wireless TDMA communications systems.

We present a throughput analysis of a multi-address call extraction server in F-NET. The extraction server splits a multi-address call into individual calls. Since the actual operation mechanisms of the server are complicated, it is difficult to directly apply the standard Markov chain technique. Restricting ourselves to the case where the server is offered by a saturated input process, we propose a simple probabilistic method to investigate the departure process of the server and its asymptotic behavior. Numerical examples evaluated by the method are compared with simulations, which demonstrate the accuracy of our modeling approach.

A generalized conservation law for mixed preemptive and nonpreemptive discipline is presented. In this discipline there are N job classes which are assigned preemptive resume priority and each job class split into Nj(j0, , N) job subclasses which are assigned head-of-the-line priority. The discipline is used, e.g., in communication control in a switching system. We give a proof for the conservation law by an intuitively comprehensive direct method, which is also applied for the Kleinrock's conservation law to make his proof elaborated. An alternative proof for Takahashi's conservation law on preemptive-resume M GI/G1 G2/1 systems is also presented to clarify the physical meaning in the connection with completion times.

We propose a finite-capacity single-vacation model, with close-down/setup times and a Markovian arrival process (MAP), for SVC-based IP-over-ATM networks. This model considers the SVC processing overhead and the bursty nature of IP packet arrivals. Specifically, the setup time corresponds to the SVC setup time and the vacation time corresponds to the SVC release time, while the close-down time corresponds to the SVC timeout. The MAP is a versatile point process by which typical bursty arrival processes like the IPP (interrupted Poisson process) or the MMPP (Markov modulated Poisson process) is treated as a special case. The approach we take here is the supplementary variable technique. Compared with the embedded Markov chain approach, it is more straightforward to obtain the steady-state probabilities at an arbitrary instant and the practical performance measures such as packet loss probability, packet delay time, and SVC setup rate. For the purpose of optimal design of the SVC-based IP-over-ATM networks, we also propose and derive a new performance measure called the SVC utilization ratio. Numerical results show the sensitivity of these performance measures to the SVC timeout period as well as to the burstiness of the input process.

We propose a traffic measurement system which uses trap and polling methods. To obtain its performance we consider a queueing model with a single server and evaluate a packet delay. In our multi-cast traffic, packets are modeled as a batch with a batch size distribution {gk}. The batch arrival process is observed as two processes on the basis of batch size. For a batch whose size is more than or equal to a threshold L, the batch will be trapped by our traffic measurement system (in queueing model, it will enter a queue immediately after its arrival). For a batch whose size is less than L, it will be observed at a polling cycle T (in queueing model, it will be temporarily stored in a buffer and all these small batches will be cyclically noticed with a cycle T). We analyze this queueing model by a diffusion approximation and compare the packet delay observed by our traffic measurement system with the L=1 original batch arrival model. Evaluating the results of the diffusion approximation, we illustrate that our traffic measurement system has functions not only to give an accurate estimation of the mean waiting time but also reduce the number of measurements by choosing appropriate parameters L and T.

In a telecommunication network system, a scheme for reforwarding call-terminating setup messages (SETUP messages) is used to guard against their loss. We have developed a method for evaluating the loss probability of these reforwarding schemes. We started with a stochastic model in which the messages are reforwarded after a constant time span from the time that the first messages have been forwarded. This model corresponds to the finite-capacity BPP/M/1/m model. We showed a method for calculating the "timeout" probability. We then added an approximate method for calculating the loss probability. Finally, using the proposed methods, we clarified the existence of the best reforwarding timelag.

This paper presents an analysis for a multi-server system with batch arrivals of queueing and non-queueing types of customers. Customers of two types are assumed to arrive in two independent batch Poisson streams and to have exponentially distributed service times. This situation can be seen in the Facsimile Intelligent Communication System (FICS). The existing studies on the service systems which dealt with two types of customers, however, were limited to the case of Poisson arrivals. By using the generating function technique, a recursive scheme for the steady-state probabilities in the system is obtained. Traffic measures, e.g., loss probability, mean waiting time, and the probability that the number of customers in the system is zero, are deduced without any truncated error. It is shown that the above-mentioned traffic measures can be represented by only a finite set of the steady-state probabilities in spite of the infinite state space. In some special cases, it is seen that the results obtained here are consistent with the previous works. Numerical examples are shown and traffic characteristics are also discussed.

We present our design and operation of a 6-bit quasi-triangle voltage waveform generator comprising three circuit blocks; an improved variable Pulse Number Multiplier (variable-PNM), a Code Generator (CG), and a Double-Flux-Quantum Amplifier (DFQA). They are integrated into a single chip using a niobium Josephson junction technology. While the multiplication factor of our previous m-bit variable-PNM was limited between 2m-1 and 2m, that of the improved one is extended between 1 and 2m. Correct operations of the 6-bit variable-PNM are confirmed in low-speed testing with respect to the codes from the CG, whereas generation of a 6-bit, 0.20mVpp quasi-triangle voltage waveform is demonstrated with the 10-fold DFQA in high-speed testing.

This paper develops a closed form approximation method for the mean performance measures in a single-server priority queue with batch arrivals of two classes. The batch arrivals queueing model considered here is an extension of the previously analyzed models and it has a potential applicability in packet communication systems. The interarrival time of batches, batch size (the number of customers) and service time of customers are assumed to have a general distribution for each priority class. The head-of-the-line (HL) and preemptive-resume (PR) rules are considered. Qualitative characterization results are presented through a flow-balance argument. Especially, important relationships between the mean performance measures are derived, which enable us to make an approximation. Using a diffusion approximation for the unfinished work and its refinement, and using the qualitative results, new approximate formulas for the mean performance measures, e.g., mean delay time of each priority class are obtained. Some numerical examples are provided and compared with exact and simulation results, confirming the accuracy of the approximation. The proposed approximate formulas are shown to be exact if the arrival streams for both classes are batch Poisson processes.

This paper presents a queueing analysis method for the M/M/1 queue with service interruptions. The queueing model considered here is applicable to voice/data communication systems, communication swiching systems and so on. Assuming that both on- and off-periods of the server are generally distributed, the steady-state distribution of the number of customers in the system, including one unknown function, is derived by using the supplementary variable technique. The mean number of customers in the system is obtained by approximating one unknown parameter. The proposed approximate formula requires only the first two-moment input parameters, which is simple enough for numerical calculations. Some numerical examples are compared with the exact and simulated results and show good accuracy of the proposed formula for a practical situation.

A multi-server system with trunk reservation is studied. The system is offered by two types of customers (class-1 and class-2). They arrive in independent batch Poisson streams and have an exponentially distributed service time. Class-1 customers will be lost or rejected if they find all S servers busy on their arrivals. Class-2 customers will use at most S'=S-R servers and enter a queue with N capacity if they find the number of idle servers less than or equal to R on their arrivals. Here, R is the number of reserved servers for class-1 customers. An example of the system is realized in NTT's facsimile communications network F-NET.