In this paper, we will clarify the problem of consecutively lost customer due to buffer overflow in an IPP, M/M/l/K queueing system including an M1, M2/M/l/K queueuing system as a special case. We define a length of a consecutive loss as the number of customers consecutively lost due to buffer overflow. And, we obtain individual distributions of the lengths of consecutive losses for the IPP- and Markov-sources. From analytical and numerical results, it is shown that either they are geometrical or they can be approximated by a geometric distribution. Also, from numerical examples, we show some properties of the length of consecutive customer loss.

It has been shown that the performances of single-receiver ARQ schemes are largely dependent on the packet-error process, i.e., for dependent packet-error environment, they are under- or over- estimated by analyzing them under the assumption that packet-errors occur at random. While, multi-receiver ARQ's have not been analyzed and evaluated for dependent packet-error process. In this paper, we analyze the throughput efficiency of the fundamental multi-receiver Go-back-N ARQ scheme, which can be implemented very simply, over an unreliable channel modeled by the two-state Markov process. Any receiver erroneously receives a packet with probability inherent to each state. From numerical results, we show that the throughput efficiency of the fundamental multi-receiver Go-Back-N ARQ scheme depends on the number of receivers, round-trip-delay, and the characteristic of the Markov process. Also we show that the throughput efficiency of the fundamental multi-receiver Go-Back-N ARQ scheme for larger decay factor and larger difference between packet error probability at each state is considerably better than that for the random error pattern.

We consider a communication system in which a transmitter is connected to a receiver through parallel channels, and the Go-Back-N ARQ scheme is used to handle transmission errors. A packet error on one channel results in retransmission of packets assigned to other channels under the Go-Back-N ARQ scheme. Therefore, the channel-grouping (a grouped-channel is used to transmit the same packet at a time), would affect the throughput performance. We analyze the throughput performance, and give a tree-algorithm to efficiently search for the optimal channel-grouping which makes the throughput to become maximum. Numerical results show that the throughput is largely improved by using the optimal channel-grouping.

Recently, the throughput performances of ARQ's have been analyzed over a Markov error channel. It has been shown that given a round-trip-delay, the throughput of the Stop-and-Wait ARQ is dependent only on the overall average packet-error probability. In this paper, we exactly analyze the Stop-and-Wait ARQ scheme under the condition that the channel is slotted and packet errors occur according to a two-state Markov chain which is characterized by the decay factor. The distribution of packet delay time and the channel usage factor are obtained. From the analytical results and numerical examples, it is shown that for a given round-trip-delay, the average packet delay time and the channel utilization factor depend on both the overall average packet-error probability and the decay factor characterizing the two-state Markov chain. Furthermore, the decay factor gives different influence on the average delay time and the channel usage factor depending on whether the round-trip-delay is even slots or not.

This paper studies the performance of a dialogue communication system which consists of two stations over a half-duplex line. When a station seizes the right to send its packets, it can consecutively transmits k packets. We analyze the transmission time of a message and the throughput performances of Stop-and-Wait, Go-back-N and Selective-Repeat protocols for the half-duplex line transmission system. Based on the analytical and numerical results, we clarify the influences of the switching and the thinking times, which exist in half-duplex line system, on the throughput performance, and give the optimal k which makes the throughput to become maximum. It is observed that the throughput performances are greatly influenced not only by the switching and thinking times but also by the average message length.

In this paper, we investigate the throughput efficiency of the Go-Back-N ARQ protocol on parallel multiple channels with burst errors. We assume that packet errors occur according to a two-state Markov chain on each channel. The effect of the decay factor of the Markov chain on throughput efficiency is evaluated based on the results of numerical analysis.

Go-Back-N automatic repeat request (GBN ARQ) and Stop-and wait (SW) ARQ schemes are one of fundamental and widely used error control procedures for data communication and computer communication systems. The throughput and delay performances of these ARQ schemes have been analyzed for a random error channel, which could not applicable for a radio channel, for example. In this paper, considering the correlated, noisy channel, we derive the exact formula for the delay of a frame in GBN and SW ARQ schemes. First, the delay formula for the discrete time M[x]/G/1 queueing system with starter. Next, the virtual service time of a frame is found in terms of the decay factor of a two-state Markov chain. As a result, it is shown that the performance of the delay is improved with the larger decay factor.

In this paper, to investigate the processing requirements at each node and offered network load of receiver-based and router-based protocols, we analyze the number of packet transmissions on each link until all receivers receive a packet for an arbitrary multicast-tree topology and packet loss probability considering the correlation between loss events of a packet for different receivers. In order to show the effectiveness of the analytical results, we demonstrate the numerical examples for various conditions. The numerical results show that local recovery protocols, especially router-based protocol can reduce the offered network load due to data packets and their acknowledgements, and can decentralize processing requirement of sending nodes effectively. Further, we reveal the influence of the locations of group senders on the performance of both protocols.

To improve the throughput efficiencies of ARQ protocols over a high random packet-error channel, contiguous multiple copy-transmission (CMCT) strategy for which each packet is (re-)transmitted by sending its multiple copies in contiguous slots has been used so far. However, in burst error environments, all copies may be damaged in an error burst resultting the performance degradation of CMCT. To cope with this situation, we propose, in this paper, a new strategy called intermittent multiple copy-transmission (IMCT) whereby multiple copies are sent at a fixed interval. The throughput efficiency of go-back-N ARQ using CMCT or IMCT is analyzed and considered under a two-state Markov channel model expressing burst error property of a channel. As a result, it is shown that (i) the degree of improvement of throughput efficiency by CMCT or IMCT depends on the degree of error burst and (ii) the proposed IMCT can improve the throughput efficiency of go-back-N ARQ for high and burst error channels.

In this paper, we analyze the throughput of the Stop-and-wait and Go-back-N ARQ schemes over an unreliable channel modeled by the two-state Markov process. Generally, in these states, block error probabilities are different. From analytical results and numerical examples, we show that the throughput of the Stop-and-wait ARQ scheme only depends on overall average error probability, while that of the Go-back-N ARQ scheme depends on the characteristic of the Markov process.

The basic selective-repeat ARQ scheme can achieve very high throughput. However, it encounters a resequencing problem. We analyze the average resequencing delay approximately under the assumption that the arrivals of NAK's are totally independent of the past history of the system. And, we examine its characteristics from numerical examples.

In this paper, we propose an adaptive Go-Back-N (GBN) ARQ protocol over two parallel channels with slow state transition. This proposed protocol sophisticatedly determines the order of priority of the channel usage for sending packets, by using the channel-state feedback information. We exactly analyze the throughput efficiency of the protocol and obtain its closed-form expression under the assumption that the time-varying channel is modeled by a two-state Markov chain, which is characterized by packet error rate and the decay factor. The analytical results and numerical examples show that, for a given round-trip time, the throughput efficiency depends on both the average packet-error rate and the decay factor. Furthermore, it is shown that the throughput efficiency of the proposed protocol is superior to that of the non-adaptive Go-Back-N protocol using the two channels in a fixed order in the case of slow state transition (i.e. the decay factor is positively large).

In high-speed packet networks, protocol processing overhead time becomes remarkable in determining the system performance. In this paper, we present a new Selective-Repeat ARQ scheme (called Block SR-ARQ sheme), in which a packet is transmitted or retransmitted in the same way as basic SR-ARQ scheme, but a single acknowledgement packet is used to acknowledge a block of packets. The maximum number of packets acknowledged by an acknowledgement packet is defined as block size. We analyze the system throughput and the average packet delay over the system, and the accuracy of approximately analyzed results is validated by simulation. Furthermore, we show that there exists an optimal block size which obtains both the maximum throughput and the minimum average packet delay.