Buffer Behavior for Mixed Arrivals and Single Server with Random Interruptions

A queueing model with finite buffer size, mixed input traffic (Poisson and burst Poisson arrivals), synchronous transmission and server interruptions through a Bernoulli sequence of independent random variables is studied. Using average burst length, traffic intensity and input traffic mixture ratio as parameters, the relationships among buffer size, overflow probability and expected message queueing delay are obtained. An integrated digital voice-data system with synchronous time division multiplexing (STDM) for a large number of voice sources and mixed arrival process for data messages is considered as an application for this model. The results of this study are portrayed on graphs and may be used as guidelines in buffer design problems in digital voice-data systems. The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well.     

Buffer Behavior for Mixed Input Traffic and Single Constant Output Rate

A queueing model with limited waiting room (buffer), mixed input traffic (Poisson and compound Poisson arrivals), and constant service rate is studied. Using average burst length, traffic intensity, and input-traffic mixture rate as parameters, we obtain relationships among buffer size, overflow probabilities, and expected message-queueing delay due to buffering. These relationships are portrayed on graphs that can be used as a guide in buffer design. Although this study arose in the design of statistical multiplexors, the queueing model developed is quite general and may be useful for other industrial applications.     

Towards the formation of comprehensive SLAs between heterogeneous wireless DiffServ domains

Traffic patterns generated by multimedia services are different from traditional Poisson traffic. It has been shown in numerous studies that multimedia network traffic exhibits self-similarity and burstiness over a large range of time-scales. The area of wireless IP traffic modeling for the purpose of providing assured QoS to the end-user is still immature and the majority of existing work is based on characterization of wireless IP traffic without any coupling of the behaviour of queueing systems under such traffic conditions. Work in this area has either been limited to simplified models of FIFO queueing systems which do not accurately reflect likely queueing system implementations or the results have been limited to simplified numerical analysis studies. In this paper, we advance the knowledge of queueing systems by example of traffic engineering of different UMTS service classes. Specifically, we examine QoS mapping using three common queueing disciplines; Priority Queuing (PQ), Low Latency Queuing (LLQ) and Custom Queueing (CQ), which are likely to be used in future all-IP based packet transport networks. The present study is based on a long-range dependent traffic model, which is second order self-similar. We consider three different classes of self-similar traffic fed into a G/M/1 queueing system and construct analytical models on the basis of non-preemptive priority, low-latency queueing and custom queueing respectively. In each case, expressions are derived for the expected waiting times and packet loss rates of different traffic classes. We have developed a comprehensive discrete-event simulator for a G/M/1 queueing system in order to understand and evaluate the QoS behaviour of self-similar traffic and carried out performance evaluations of multiple classes of input traffic in terms of expected queue length, packet delay and packet loss rate. Furthermore, we have developed a traffic generator based on the self-similar traffic model and fed the generated traffic through a CISCO router-based test bed. The results obtained from the three different queueing schemes (PQ, CQ and LLQ) are then compared with the simulation results in order to validate our analytical models.     

Analysis on Partial Overflow Queueing Systems with Two Kinds of Calls

In this paper, the traffic model of one kind of the partial overflow system is presented and theoretically analyzed, which has remained unsolved up to today. In the partial overflow systems, the considered overflow traffic stream is a part of the traffic stream overflowing from a common trunks group with multiinput calls. The systems with two kinds of calls are treated. Both of the two input traffic streams are assumed to follow the Poisson process and the holding times of the calls are assumed to be identical and follow an exponential distribution. Under these assumptions, analytical formulas are derived to calculate the individual traffic characteristics for both the loss-loss partial overflow system and the wait-loss partial overflow system. With these results, the accuracy of the well-used equivalent random theory in approximating the traffic model offered with partial overflow stream is investigated. The two-input model is a general one and can be used for analyzing the model with more than two inputs. It is expected that the formulas derived in this paper can be Used to improve the accuracy of ERT method as well as used directly.     

PERFORMANCE ANALYSIS OF HETEROGENEOUS TRAFFIC ON AN INTEGRATED NETWORK LINK WITH FINITE WAITING ROOM AND ANTICIPATED-RELEASE RESERVATION POLICY

We consider a system where the superposition of two heterogeneous Poisson traffic streams is offered to an integrated network link in synchronous transfer mode, where one stream follows the blocked-and-cleared mode (‘loss’ mode) and the other can wait (finitely) if bandwidth is not available for connection at the time of arrival (‘hold’ mode). We assume that each stream has different bandwidth requirements per call. A reservation scheme, called anticipated-release policy, is introduced where an arrival is accepted into a waiting room only if the amount of time this customer is expected to wait is within acceptable limits. For such a loss/hold system, we provide analytical performance models for exponential service time distributions for both streams as well as for the non-exponential service time distribution case for the traffic stream in ‘hold’ mode. We also present a method on how to model the waiting time distribution of the traffic stream with ‘hold’ mode. From numerical studies, we observe that blocking can be reduced considerably for both services just by introducing a small waiting room for one traffic class compared to ‘loss’ mode for both traffic classes. Furthermore, this holds true for the case when a maximum tolerable time limit is imposed on the waiting. Finally, our results indicate that this loss/hold scenario with limited waiting room appears to be virtually insensitive to the service time distribution of the ‘hold’ mode traffic.     

The analysis of a queue arising in overflow models

A methodology is presented for analyzing a queuing submodel which frequently arises in the study of overflow models. In this submodel a finite capacity, multiserver queue with exponentially distributed service times, and arriving traffic consisting of a Poisson parcel and several overflow parcels, are assumed. By modeling the overflow parcels as interrupted Poisson processes, an exact queuing analysis is possible. The analysis yields the steady-state queue length distribution, and for each input parcel: (1) the steady-state queue length distribution at arrivals; (2) the probability that an arriving call is blocked (parcel blocking); and (3) the waiting time distribution of an arriving call, in addition to a complete characterization of the overflow due to each parcel     

Queueing Models for Computer Communications System Analysis

Modeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in today's computer communications demand our intensive effort to enhance the modeling capability. The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems. First we review basic properties of exponential queueing systems, and then give an overview of recent progress made in the areas of queueing network models and discrete-time queueing systems. A unified treatment of buffer storage overflow problems will be discussed as an application example, in which we call attention to the analogy between buffer behavior and waiting time in theGI/G/1queue. Another application deals with the analysis of various multiplexing techniques and network configuration. An extensive reference list of the subject fields is also provided.     

Finite Buffer Behavior with Poisson Arrivals and Random Server Interruptions

A queueing model with finite buffer size, Poisson arrival process, synchronous transmission and server interruptions is studied through a Bernoulli sequence of independent random variables. An integrated digital voice-data system with Synchronous Time-Division Multiplexing (STDM) for voice sources and Poisson arrival process for data messages is considered as an application for this model. The relationships among overflow probabilities, buffer size and expected queueing delay due to buffering for various traffic intensities are obtained. The results of this study are portrayed on graphs and may be used as guide lines for the buffer design in digital voice-data systems. Although this study arose in the design of a buffer for digital voice-data systems, the queueing model developed is quite general and may be useful for other industrial applications.     

Approximation of loss calculation for hierarchical networks with multiservice overflows

This paper studies loss calculation in hierarchical networks with multiservice overflows which have different call arrival rates, mean holding times, bandwidth requirements and share a common link. The loss calculation involves two challenging problems: 1) the computation of the two moment characterizations of multiservice overflow traffic over the shared link, 2) the calculation of the loss probabilities for multiservice non-Poisson overflow traffic in hierarchical systems. An efficient approximation method, known as multiservice overflow approximation (MOA), is proposed to enable multiservice networks designs with hierarchical architecture. Two contributions are included in the MOA method. First, an approximation based on blocking probabilities matching is proposed to compute the variances of multiservice overflows over the shared link. Second, a modified Fredericks & Hayward's approximation is used to calculate the loss probabilities of multiservice non-Poisson over flow traffic. The performance of the MOA method is evaluated in a two-tier hierarchical cellular network and compared with an existing approximation method based on multi-dimensional Markov-modulated Poisson process (MMPP). Verified by simulations, the MOA method achieves better accuracy in the general heterogeneous cases at lower computational cost than the MMPP method.     

Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process

Recent measurements of packet/cell streams in multimedia communication networks have revealed that they have the self-similar property and are of different characteristics from traditional traffic streams. In this paper, we first give some definitions of self-similarity. Then, we propose a fitting method for the self-similar traffic in terms of Markov-modulated Poisson process (MMPP). We construct an MMPP as the superposition of two-state MMPPs and fit it so as to match the variance function over several time-scales. Numerical examples show that the variance function of the self-similar process can be well represented by that of resulting MMPPs. We also examine the queueing behavior of the resulting MMPP/D/1 queueing systems. We compare the analytical results of MMPP/D/1 with the simulation ones of the queueing system with self-similar input.     

An analysis of the performance of ARQ schemes for integrated traffic satellite-switched SFH and DS CDMA networks

The delay and throughput performance of satellite-switched Slow Frequency Hopping CDMA network for simultaneous voice and data transmission is analyzed and compared to that of a DS-CDMA system. Two ARQ schemes are suggested for data while Forward Error Correction using the same encoder is used for voice packets. The queueing analysis assumes priority for voice and two models for voice traffic are used (Markovian and IPP). The probability of successful packet transmission is derived for all systems as a function of traffic load allowing us to evaluate the systems using delay, throughput, and voice packet loss as figures of merit. Numerical results show that while voice delay is minimal DS CDMA is much more effective then SFH CDMA in all cases. One interesting result is that SFH systems perform better with S/W schemes and achieve a higher maximum throughput. It is also observed that the IPP and Markovian models gave similar results.This work was supported by an NSERC CRD (Collaborative Industrial Research and Development grant,) with Spar Aerospace, Quebec, Canada     

Jitter analysis of an IPP tagged traffic stream in an {IPP,M}/M/1 queue

We study a single server queue with two different arriving streams, a tagged arrival process and a background arrival process. The tagged traffic is assumed to be an interrupted Poisson process (IPP) and the background traffic is Poisson. The service time is exponentially distributed, and customers are served in a FIFO manner. We obtain numerically the probability density function of the inter-departure time of the IPP tagged arrival process, from which we calculate its jitter, defined as a percentile of the inter-departure time. Numerical results of the 95th percentile and the squared coefficient of variation of the tagged inter-departure time are given as a function of the arrival rate of the background traffic.     

Performance Analysis of Reassembly and Multiplexing Queueing with Long-Range-Dependent Input Traffic

This paper studies the impact of long-range-dependent (LRD) traffic on the performance of reassembly and multiplexing queueing. A queueing model characterizing the general reassembly and multiplexing operations performed in packet networks is developed and analyzed. The buffer overflow probabilities for both reassembly and multiplexing queues are derived by extending renewal analysis and Bene fluid queue analysis, respectively. Tight upper and lower bounds of the frame loss probabilities are also analyzed and obtained. Our analysis is not based on existing asymptotic methods, and it provides new insights regarding the practical impact of LRD traffic. For the reassembly queue, the results show that LRD traffic and conventional Markov traffic yield similar queueing behavior. For the multiplexing queue, the results show that the LRD traffic has a significant impact on the buffer requirement when the target loss probability is small, including for practical ranges of buffer size or maximum delay.     

On the Calculation of Overflow Systems with a Finite Number of Sources and Full Availiable Groups

This paper deals with the calculation of loss probabilities in overflow systems with a finite number of sources and full available groups. An exact, explicit solution is derived for overflow systems with only one primary group. Furthermore, an exact method is applied in case of overflow systems with two primary groups. For overflow systems with an arbitrary number of primary groups an approximate method is developed which takes into account the variance of offered overflow traffic. This approximate method yields results which are in good agreement with exact calculations and simulation results.     

Trafic d’un nombre limité de sources mélangeant attente et perte

We consider a multiserver queueing system carrying traffic from a finite-size population (Engset model). When faced with congestion, some of the requests vanish (lost calls), while the others are allowed to wait for a free server, resulting in a mixed (waiting + loss) system. Grade of service requirements lead to calculate loss probability and waiting time distribution — since standards usually upperbound waiting times.     

Performance Modeling for Packet Networks with Satellite Overflow Channels

In a packet network using medium speed terrestrial connectivity, average end-to-end delay can be reduced by using highspeed satellite overflow channels despite their propagation delay. To investigate networks of this type analytically, we derive a new basic queueing model for overflow systems with buffered traffic. The simple, closed-form expressions facilitate analysis. Approximations are developed for multiple primary systems with a single overflow channel; these agree with simulation. Using the overflow model analysis indicated the following. The reduced queueing delay to the high capacity overflow channel more than compensated for propagation delay. Inherent, broadcast transmission capabilities of satellite channels reduced overall network delay. The high capacity overflow channels permit networks to withstand substantial nodal imbalance and overloads.     

Solving some overflow traffic models with changed serving intensities

This paper investigates specific systems with overflow traffic. A primary group with two Poisson traffics is considered whereupon the rejected calls from one traffic are directed to the alternative group with changed serving intensities. The generating function technique is used for analytical solving the model with secondary and ternary groups and the model that separately treated the channels in alternative groups. The obtained analytical solutions essentially reduce the constraints concerning the equation system size, convergence, and calculation time, which arise when numerically solving the steady-state system equations. For the case with single channels in the ternary group, explicit solutions for traffic parameters are obtained. Also, comparison with the model that has a unique serving intensity of overflow traffic is made.     

Modeling of systems with overflow multi-rate traffic

The article proposes an analytical method for determining occupancy distribution and blocking probability in systems which are offered overflow traffic composed of multi-service traffic streams. The described analytical model enables determination of parameters of traffic overflowed from primary groups in hierarchically constructed telecommunication networks. The proposed method is based on an appropriate modification of the Kaufman-Roberts recursion for the full-availability group with multi-rate traffic and uses the modified Fredericks & Hayward’s approximation. Additionally, an approximate method for dimensioning systems with multi-service overflow traffic is also presented. The analytical results of the blocking probability and the results obtained in the dimensioning processes calculated using the presented methodology are compared with the data obtained from the system simulation process.     

Closed-form solutions for key performance measures of packet multiplexers with finite capacity queue

We revisit the packet multiplexer with a discrete-time single server queue of limited capacity, and we derive a set of exact closed-form solutions for the major performance measures, such as the distributions of queue length, waiting time and number of lost packets per arriving batch. Assuming equally utilised inputs, the results refer to batch arrivals of binomial and Poisson distributed size, whereas they generally hold for systems with two inputs. The analysis is based on both the commonly used Early Arrival and Late Arrival queueing models, and we show that these models are equivalent at any capacity in terms of both waiting time and loss probability if the Late Arrival queue can hold one additional packet compared to its Early Arrival counterpart.     

Optimal choice of Reed-Solomon codes to protect against queuing losses in wireless networks

This article proposes algorithms to determine an optimal choice of the Reed-Solomon forward error correction (FEC) code parameters (n,k) to mitigate the effects of packet loss on multimedia traffic caused by buffer overflow at a wireless base station. A network model is developed that takes into account traffic arrival rates, channel loss characteristics, the capacity of the buffer at the base station, and FEC parameters. For Poisson distributed traffic, the theory of recurrent linear equations is applied to develop a new closed form solution of low complexity of the Markov model for the buffer occupancy. For constant bit rate (CBR) traffic,an iterative procedure is developed to compute the packet loss probabilities after FEC recovery.