• Journal of applied mathematics & informatics
• /
• 제33권1_2호
• /
• pp.185-191
• /
• 2015

This paper considers a discrete-time buffer system with session-based arrivals, an infinite storage capacity and one unreliable output line. There are multiple different types of sessions and the output line is governed by a finite state Markov chain. Based on a generating functions approach, we obtain an exact expression for the mean buffer content.

• 한국통신학회논문지
• /
• 제28권9B호
• /
• pp.783-792
• /
• 2003

We consider a finite-buffer discrete-time queueing system with fixed-size bulk-service discipline: Geo/ $G^{B}$1/K＋B. The main purpose of this paper is to present a performance analysis of this system that has a wide range of applications in Asynchronous Transfer Mode (ATM) and other related telecommunication systems. For this purpose, we first derive the departure-epoch probabilities based on the embedded Markov chain method. Next, based on simple rate in and rate out argument, we present stable relationships for the steady-state probabilities of the queue length at different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of number of packets in the system at three different epochs and the loss probability. The numerical results are presented for a deterministic service-time distribution - a case that has gained importance in recent years.s.

• 대한수학회지
• /
• 제40권1호
• /
• pp.87-107
• /
• 2003

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.285-295
• /
• 2001

We consider a queueing system under overload control to support bursty traffic. The queueing system under overload control is modelled by MMBP/D1/K queue with two thresholds on buffer. Arrival of customer is assumed to be a Markov-modulated Bernoulli process (MMBP) by considering burstiness of traffic. Analysis is done in discrete-time case. Using the generating function method, we obtain the stationary queue length distribution. Finally, the loss probability and the waiting time distribution of a customer are given.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제5권6호
• /
• pp.1147-1165
• /
• 2011

We present a simple and cost effective rate control scheme for streaming video over a wireless channel by using the information of mobile devices' buffer level. To prevent buffer fullness and emptiness at receivers, the server should be able to adjust sending rate according to receivers' buffer status. We propose methods to adjust sending rate based on the buffer level and discrete derivative of the buffer occupancy. To be compatible with existing network protocols, we provide methods to adjust sending rate by changing the inter-packet delay (IPD) at the server side. At every round-trip time, adjustments of sending rate are made in order to achieve responsiveness to sudden changes of buffer availabilities. A series of simulations and the prototype system showed that the proposed methods did not cause buffer overflows and it can maintain smoother rate control and react to bandwidth changes promptly.

• 산업경영시스템학회지
• /
• 제42권4호
• /
• pp.91-105
• /
• 2019

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

• Journal of Communications and Networks
• /
• 제16권2호
• /
• pp.193-201
• /
• 2014

In cognitive radio networks, the packet transmissions of the secondary users (SUs) can be interrupted randomly by the primary users (PUs). That is to say, the PU packets have preemptive priority over the SU packets. In order to enhance the quality of service (QoS) for the SUs, we propose a spectrum access strategy with an ${\alpha}$-Retry policy. A buffer is deployed for the SU packets. An interrupted SU packet will return to the buffer with probability ${\alpha}$ for later retrial, or leave the system with probability (1-${\alpha}$). For mathematical analysis, we build a preemptive priority queue and model the spectrum access strategy with an ${\alpha}$-Retry policy as a two-dimensional discrete-time Markov chain (DTMC).We give the transition probability matrix of the Markov chain and obtain the steady-state distribution. Accordingly, we derive the formulas for the blocked rate, the forced dropping rate, the throughput and the average delay of the SU packets. With numerical results, we show the influence of the retrial probability for the strategy proposed in this paper on different performance measures. Finally, based on the trade-off between different performance measures, we construct a cost function and optimize the retrial probabilities with respect to different system parameters by employing an iterative algorithm.

• ETRI Journal
• /
• 제28권3호
• /
• pp.301-310
• /
• 2006

In mobile communications, a class of variable-complexity algorithms for convolutional decoding known as sequential decoding algorithms is of interest since they have a computational time that could vary with changing channel conditions. The Fano algorithm is one well-known version of a sequential decoding algorithm. Since the decoding time of a Fano decoder follows the Pareto distribution, which is a heavy-tailed distribution parameterized by the channel signal-to-noise ratio (SNR), buffers are required to absorb the variable decoding delays of Fano decoders. Furthermore, since the decoding time drawn by a certain Pareto distribution can become unbounded, a maximum limit is often employed by a practical decoder to limit the worst-case decoding time. In this paper, we investigate the relations between buffer occupancy, decoding time, and channel conditions in a system where the Fano decoder is not allowed to run with unbounded decoding time. A timeout limit is thus imposed so that the decoding will be terminated if the decoding time reaches the limit. We use discrete-time semi-Markov models to describe such a Fano decoding system with timeout limits. Our queuing analysis provides expressions characterizing the average buffer occupancy as a function of channel conditions and timeout limits. Both numerical and simulation results are provided to validate the analytical results.

• Industrial Engineering and Management Systems
• /
• 제4권2호
• /
• pp.117-122
• /
• 2005

An assembly system (AS), a valuable tool for mass production, is generally composed of a number of workstations and a transport system. While the workstations perform some preplanned operations, the transport system moves the assemblies by special designed pallets from one station to another. One common problem associated with automatic assembly systems is that some assembly operations may have relatively long cycle times. As a consequence, the productivity, as determined by the operations with the longest cycle time, can be reduced significantly. Therefore, special forms of parallel workstations were developed to improve the performance of an assembly system. In this paper, three most commonly used parallel stations: on-line, off-line and tunnel-gated stations in a free transfer assembly system are studied via discrete event simulation. Our findings revealed that the off-line parallel system has the best performance because the two independent parallel stations can lower the buffer requirement; reduce the sensitivity to variability of processing time and balance of a line. On-line parallel systems were found to have a relatively poor performance, because the operations of two parallel stations block each other, and higher buffer capacity is required to achieve similar capacity. The tunnel-gated system was more efficient than the on-line system since the first parallel station can operate independently. More importantly, we have quantified the productivity of the three different strategies mentioned. Engineers can choose the optimal strategies for installing parallel stations under their working environment.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.153-162
• /
• 2010

The finite buffer GI/G/1/K system is set up by using an unconventional arrangement of the state space, in which the remaining interarrival time or service time is chosen as the level. The stationary distributions of resulting Markov chain can be explicitly determined, and the chain is positive recurrent without any restriction. This is an advantage of this method, compared with that using the elapsed time approach [2].