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 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.

This paper clarifies the appropriate traffic domains for combination between two database schemes (i. e. , HLR database scheme and VLR database scheme) and two call routing schemes (i. e. , Redirection Routing scheme and Look-a-head Routing scheme) in the Global Mobility Network (GLOMONET), which is able to provide global roaming service for the personal telecommunication user. The appropriate domains for combination between each scheme are shown to depend on user's mobility (i. e. the frequency of a user's access to a network where the user stays, the length of the period during which the user stays in the same network). Whether the appropriate domains for the HLR database scheme exist depends only on the frequency of the user's access to the network. When there are appropriate domains for the HLR database scheme, increasing the frequency of the user's access to the network, decreasing the length of the period the user stays in the user's home network, or increasing the length of the period the user stays in a network that isn't the user's home network widens the domains where the VLR database scheme is appropriate.

In Perosonal communication systems (PCS), reduction control of call blocking rate on wireless-environments, especially in terminating-call set up, is one of the key technologies to design network architecture. This is because the error rate of transferred messages there is normally much higher than that in wired environments. Terminating-call reforwarding technologies, to forward twice terminating-call messages through paging channels depending on call states, would be essential under such conditions, and in the PCS network architecture there are two possible reforwarding schemes: network-assisted reforwarding (NAR) and cell-station-assisted reforwarding (CAR). We first propose a traffic model for evaluating the performance of terminating-call reforwarding from the viewpoint of reduction of the call blocking rate on PCS, and then we clarify the advocating domains for NAR and CAR. Finally, we present a case study using this evaluation model for the Personal Handy-phone System (PHS), which is a PCS in Japan. The results of this study confirm that NAR is more efficient than CAR.

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.

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.