We study three different discrete-time queueing systems, which accommodate two types of customers, named type 1 and type 2. New customers arrive independently from slot to slot, but the numbers of arrivals of both types in any slot are possibly mutually dependent; their joint probability generating function ( pgf ) is A(z1,z2). The service times of all customers are deterministically equal to one time slot. We first consider a scenario ( Option A) with one single server which is to be shared by the two customer types. Here, we assume that type-1 customers have absolute service priority over type-2 customers. Moreover, the server is subject to random server interruptions, which occur independently from slot to slot. We derive a functional equation for the steady-state joint pgf U(z1, z2) of the numbers of type-1 and type-2 customers in the system. Relying on the application of Rouch & eacute;'s theorem, we are able to explicitly solve the functional equation for arbitrary arrival pgfs A(z1,z2), but more elegant results are obtained for some specific choices of A(z1,z2). Next, we focus on two different scenarios ( Option B and Option C) where both customer types have their own dedicated server. Here, there are no service priorities involved. In Option B, the two servers experience simultaneous interruptions, whereas in Option C, only one of the servers is subject to interruptions. Again, we derive functional equations for the pgf U(z1, z 2 ). Although solving these equations for arbitrary arrival pgfs A(z1, z2) seems infeasible, we succeed in finding exact closed-form solutions for specific choices of A(z1,z2). Remarkably, the results obtained for the single-server priority system in Option A can be used to solve a specific instance of Option B, where the arrivals of both types of customers during any time slot are partly identical. It turns out that (fully or partly) identical arrivals also allow explicit solutions for Option C. In addition, we also provide other examples where the functional equations for Options B and C can be solved explicitly.

In this paper, we revisit the discrete-time two-queue randomly alternating service system, where one common server is shared by two queues by allocating the server, independently from slot to slot, with fixed probabilities to either queue. Arrivals of new customers into the two-queue system occur independently from slot to slot, but may be mutually dependent within a slot. They are characterized by the joint probability generating function (pgf) A(z1,z2) of the numbers of arrivals in both queues during one time slot. The service times of all customers are equal to exactly one time slot. We extend various existing results with respect to the queueing behavior of this system. Specifically, we show that the exact solutions that were previously found for the steady-state joint pgf U(z1, z2) of the system contents in both queues for the scenarios of independent Bernoulli arrivals, identical Bernoulli arrivals, global geometric arrivals, global geometric group arrivals, and the superposition of identical Bernoulli arrivals and global geometric (group) arrivals, are all special cases of a more general result, which is valid for a whole class of arrival pgfs A(z1,z2) that (among others) encompasses the aforementioned specific arrival scenarios. However, the defined class is much broader than this, and our new result allows the solution for entirely new arrival pgfs as well. We illustrate this abundantly with a large number of detailed examples. The proof of the general result is a mainly algebraic one and, unlike earlier studies, does not require intricate techniques from complex-function analysis.

In many queueing systems the server processes several customers simultaneously.Although the capacity of a batch, that is the number of customers that can be processed simultaneously, is often variable in practice, nearly all batch-service queueing models in literature consider a constant capacity.In this paper, we extend previous work on a batch-service queueing model with variable server capacity, where customers of two classes are accommodated in a common first-come-first-served single-server queue.We include correlation between the classes of consecutive customers, and the service times are geometrically distributed.We establish the equations that govern the system behaviour, the stability condition, and an expression for the steady-state probability generating function of the system occupancy at random slot boundaries.In addition, some numerical results are shown to study the impact of the mean service times and of the customer-based correlation in the arrival process on the performance of the queueing system.

In this paper, we study a discrete-time first-comefirst-served queueing system with a single server and two types (classes) of customers, where the (average) service time of a customer is longer if its type differs from the type of the preceding customer. As opposed to traditional literature, the different types of customers do not occur randomly and independently in the arrival stream: we include a Markovian type of correlation in the types of consecutive customers instead. We deduce the probability generating function of the system content, from which we extract various performance measures, such as the mean values of the system content and the customer delay. We demonstrate that the interclass correlation in the arrival stream has a tremendous impact on the system performance, which highlights the necessity to include it in the performance assessment of the system.

As internet traffic will further increase in coming years, the current network infrastructure will have to grow along in terms of capacity. To this end, optical packet/burst switching have been proposed, allowing more efficient use of the available fiber capacity. To resolve packet contention in the involved optical switches, Fiber Delay Lines (for delay assignment) and wavelength converters (for wavelength conversion) are used to reschedule the contending packets, by means of a scheduling algorithm. Existing algorithms are effective when employed with an infinite number of converters, but generally perform poorly when the number of wavelength converters is small, as is the case in most switch prototype architectures. In this paper, several parametric cost-based scheduling algorithms are proposed that take scarcity of both FDLs and converters into account. Results obtained by Monte Carlo simulation show that these algorithms not only enable improved performance (in terms of packet loss probability), but also reduce the usage of the wavelength converters, and thus, the switch's overall energy consumption.

Generalized Processor Sharing (GPS) is a simple, flexible and fair scheduling mechanism to achieve delay differentiation between several customer classes. The amount of delay differentiation is regulated by the weights given to the classes. In this paper we assume a discrete-time, two-class GPS queueing system. Our goal is to derive the optimal weights in order to minimize a weighted sum of functions of the mean delays of both classes. As analytical results are scarce we use an approximation method. The approximation is based on power series expansions of the mean queue length of each of the queues for certain weights. Padé approximants are used to extrapolate the approximation to the whole domain of possible weights, resulting in a set of approximations. An algorithm is proposed to filter out the infeasible solutions (with regard to monotonicity and other characteristics of the system) and aggregate the others, resulting in a single approximation. The result proves to be an accurate approximation of the optimal weights w.r.t. the cost function. For a load of 90% we have a maximum misprediction of 1% of the cost, in the case of a weighted sum of squares of the mean delays. The main contribution of this article is that power series approximations can be used effectively for optimization purposes.

This paper considers the detection of coded phaseshift keying signals subjected to additive white Gaussian noise and oscillator phase noise. We propose a detector that partitions the received frame into smaller blocks and models the unknown phasor variations over each block as a truncated discrete cosine transform (DCT) expansion. Detection and decoding are iteratively performed between a soft-input soft-output (SISO) demodulator, a SISO demapper, and a SISO decoder based on the sum-product algorithm and the factor graph framework, whereas the expectation-maximization algorithm is used in the demodulator for the DCT coefficients estimation. The resulting demodulator is shown to have an excellent performance/complexity tradeoff and to be well-suited for parallel processing on multiple cores.

Several diversity techniques have been proposed to cope with fading in wireless networks. A recent and promising technique, which does not increase hardware demands, is cooperative communication. Here spatial diversity is created by using other terminals to relay the information from the source terminal to the destination terminal. Cooperative protocols proposed in literature are often studied under the simplifying assumption that all channel state information is available at the destination. This contrasts to a practical scenario where channel estimates need to be derived from the broadcasted signals. In this paper, we focus on the Amplify-and-Forward protocol and use the Space-Alternating Generalized Expectation-maximization (SAGE) algorithm to estimate the channel gain and noise variance in an iterative way, exploiting both the pilot part and the data part of the signal received at the destination. We consider a relay that performs a general affine transformation on the pilot symbols received by the source, and we optimize this transformation in terms of estimation accuracy. The resulting mean square error performance is shown to be close to the Cramer-Rao lower bound (CRB).

With ever-increasing demands for bandwidth optical packet/burst switching is used to utilise more of the available capacity of optical networks. In current prototypes of optical switches time and wavelength multiplexing are combined to resolve packet contentions by means of Fiber Delay Lines and wavelength converters in the switching elements. Although optical switches have lower energy consumption than their electronic counterparts, it remains substantial. Since wavelength converters contribute significantly to the switches overall energy consumption, they should be used sparingly, rather than continuously. Current scheduling algorithms however do not take the usage of wavelength converters (and the related energy consumption) into account. To this end, we developed and evaluated new cost-based scheduling algorithms, which take both gap and delay into account to schedule an incoming packet. The performance improvement of these algorithms over existing algorithms can be traded off for a significant reduction in up-time of the wavelength converters by introducing a conversion cost in the involved cost function. This is backed by Monte Carlo simulation results, in which the algorithms are applied both in a void-filling and non-void-filling setting. The algorithms are of the same implementation complexity as current algorithms, and thus of immediate value to switch designers.

Cooperative communication systems can effectively be used to combat fading. A cooperative protocol that can be used with half-duplex terminals is the Quantize and Forward (QF) protocol, in which the relay quantizes the information received from the source before forwarding it to the destination. While the outage behavior and error performance of the QF protocol have been investigated extensively, only few research has been performed on the effects of channel parameter estimation. In this contribution, estimates are derived for all communication channels involved, while keeping the complexity of the relay terminal unaltered. First, channel estimates are calculated using known pilot symbols sent by the source and relay. Thereafter, these pilot-based channel estimates are refined using a code-aided Expectation Maximization (EM) approach, yielding an error performance that is very close to that of a system in which the channel parameters are assumed to be known.

Both optical packet switching and optical burst switching provide viable alternatives to the current electronic switching in the backbone. To resolve contention, contiguous packets/bursts are sent over different channels, and/or provided with different Fiber Delay Line (FDL) buffer delays. Typically, the resulting channel and delay selection (CDS) algorithm bases its decision on the horizon value of the different channels. Up to now, a horizon algorithm known as MING (MINimal Gap) was assumed to provide minimal loss. Relying on Markov chain-based performance modeling and a Markov decision process (MDP), we reexamine the optimality of MING. This enables us to construct CDS algorithms that outperform MING, and this for any buffer size, traffic load and packet/burst size distribution. Further, we consider burst-size-dependent and load-dependent scheduling, two stochastic mechanisms that, together with preventive dropping, enhance the algorithm's performance. The paper presents the developed method in detail, together with detailed results of the performance gain realized.

In this paper, we analyze the delay incurred by session-based traffic in the output buffer of a file server. Users can start and end sessions during which they are active and download information from the file server. Per time slot, each active user downloads a random but strictly positive number of information packets. Each session lasts for a random, yet again, strictly positive number of slots. We model the file server output buffer as a discrete-time infinite-capacity queueing system and we present an analytical technique to study the queueing delay for sessions in case of a general session-length distribution. The analysis method is based on the combination of a generating-functions approach with the use of an infinite-dimensional state description. As a result, a closed-form expression for the mean session delay is obtained. The analysis is illustrated with a numerical example, based on real traces of file server traffic.

The quality of experience (QoE) of IP-packetized streaming video is affected by both packet loss and packet delay variations. When the network delivering the video content contains a wireless link, occasional deep fades give rise to bursts of packet losses. In order to maintain a sufficient video QoE at the end user, video packets must be protected against losses by means of a suitable form of error control. In this contribution, we consider an indoor radio MIMO-OFDM transceiver operating over a Rayleigh block-fading channel with arbitrary correlation in the time and frequency dimensions, which makes use of an application layer Automatic Repeat reQuest (ARQ) protocol to provide additional protection of the video content against packet loss. We analyze the resulting residual packet loss performance, under a latency constraint imposed by the requirement of a small TV channel switching delay. This analysis makes direct use of the fading characterization (correlation functions in time and frequency dimensions) of the indoor environment, rather than relying on a Markov model that only approximately describes the packet loss process. Numerical results are obtained by Monte Carlo integration combined with an efficient importance sampling technique devised for the problem at hand. Assuming a 2.4 GHz wireless link, we point out how to select the system parameters (number of antennas, number of retransmissions) in order to achieve a residual packet loss performance yielding a satisfactory QoE for HDTV transmission.

We consider a centralised (client-server) digital TV network with heterogeneous receiver devices of different resolutions, requiring a multi-rate transport system. There exist two main ways to store and transport (streamed) TV channels in such a system: either by providing different single-layer versions of a channel (simulcast transport mode) or by keeping one multi-layered version (encoded e.g. in SVC) with extractable substreams. We propose one approximate analytical and two simulation methods to estimate the capacity demand in such a network with variable bit rate channels and we consider two behaviour models. In some TV distribution networks, the video is delivered in constant bit rate. However, this implies that the video quality is varying. In order to provide better quality of service (QoS), a network operator must deliver the channels in non-constant bit rate aiming in this way at constant video quality. Our models take into account also the correlations between the different resolutions of a channel. Starting from real experimental data, we obtain the necessary input to our models and explore two realistic TV network scenarios - with bouquets of 50 and 300 channels, respectively. The results by the three approaches correspond well (relative error of 0.5% at most). In the case of 50 channels, SVC outperforms simulcast in terms of required bandwidth, while in the case of 300 channels, SVC is outperformed by simulcast. Therefore, we conclude that it depends on the system parameters which of both transport strategies will be more beneficial to save network resources.

In optical burst switching and optical packet switching, contention of bursts (or packets) can be dealt with most effectively through a combination of wavelength conversion and optical buffering. While this is generally accepted in the optical networking community, and validated through simulation, analytic performance results for optical buffers were limited to the single-wavelength case, and the performance gain from wavelength conversion was never traced analytically for general assumptions. Quantifying this gain analytically is the scope of the current contribution. Relying on generating functions, we developed a fiber delay line (FDL) buffer model with wavelength conversion, which assumes the buffer located at the output of an optical switch, having access to multiple wavelengths. This document presents our model, validates its accuracy, and compares its output for different burst sizes (fixed or varying), scheduling policies and buffer sizes. Several numerical examples assess the applicability of our approximation, and show that our approach yields accurate results.

This paper presents three approaches to estimate the required resources in an infrastructure where digital TV channels can be delivered in unicast or multicast (broadcast) mode. Such situations arise for example in Cable TV, IPTV distribution networks or in (future) hybrid mobile TV networks. The three approaches presented are an exact calculation, a Gaussian approximation and a simulation tool. We investigate two scenarios that allow saving bandwidth resources. In a static scenario, the most popular channels are multicast and the less popular channels rely on unicast. In a dynamic scenario, the list of multicast channels is dynamic and governed by the users' behavior. We prove that the dynamic scenario always outperforms the static scenario. We demonstrate the robustness, versatility and the limits of our three approaches. The exact calculation application is limited because it is computationally expensive for cases with large numbers of users and channels, while the Gaussian approximation is good exactly for such systems. The simulation tool takes long to yield results for small blocking probabilities. We explore the capacity gain regions under varying model parameters. Finally, we illustrate our methods by discussing some realistic network scenarios using channel popularities based on measurement data as much as possible.

We propose a discrete-time queueing model for the evaluation of the IEEE 802.16e sleep-mode mechanism of Power Saving Class (PSC) I in wireless access networks. Contrary to previous studies, we model the downlink traffic by means of a Discrete Batch Markov Arrival Process (D-BMAP) with Ν phases, which allows to take traffic correlation into account. The tradeoff between energy saving and increased packet delay is discussed. In many situations, the sleep-mode performance improves for heavily correlated traffic. Also, when compared to other strategies, the exponential sleep-period update strategy of PSC I may not always be the best.

In this paper, we derive the Cramer-Rao bound (CRB) for data-aided channel estimation for OFDM with known symbol padding (KSP-OFDM). The pilot symbols used to estimate the channel are distributed over the guard interval and OFDM carriers, in order to keep the guard interval length as small as possible. An analytical expression for the CRB is obtained by performing a proper linear transformation on the observed samples. At low SNR, the CRB corresponds to the low SNR limit of the CRB obtained in [1], where it is assumed that the influence of the data symbols on the channel estimation can be neglected. At high SNR, the CRB is determined by the observations that are independent of the data symbols; the observations that are affected by data symbols are neglected. The CRB depends on the number of pilots and slightly increases with increasing guard interval length, but is essentially independent of the FFT size and the used pilot sequence. Further, a low complexity ML channel estimation technique is derived based on the linear transformation. Although in this estimation technique only a part of the observation is used, the mean squared error (MSE) performance of this estimate reaches the CRB for a large range of SNR, but a high SNR, the MSE reaches an error floor caused by the approximations made in the derivation.

We present a performance model for fiber delay line (FDL) buffers having access to multiple wavelengths on an output fiber. In optical burst switching and optical packet switching, contending bursts (or packets) need to be dealt with in an effective way, and both wavelength conversion and optical buffering are viable solutions. The buffer studied here includes both solutions, with full wavelength conversion. It is situated at the output, and handles independent arrivals. We apply an analytic discrete-time queueing model to evaluate performance in terms of loss. We mainly consider the impact of burst size (fixed or varying), scheduling policy, and buffer size. Several numerical examples assess the accuracy of our approximation, and show that our approach is applicable when burst sizes are fixed, and, when a round-robin scheduling policy is adopted, also when burst sizes vary.

We present a detailed analysis of the maximum channel utilization and loss performance in an optical buffer having access to a single outgoing channel. Such a system, consisting of a number of fiber delay lines, can only realize a discrete set of delays to resolve output port contention. This leads to an underutilization of the channel capacity, which reduces overall performance. The framework considered in this paper greatly simplifies the assumptions made in previous work, which allows us to study the impact of a variety of new parameters on the performance, e.g., the burstiness of the arrival process and the correlation of consecutive burst lengths. Moreover, we present exact results for both the channel utilization and loss rate in such a system using matrix analytic methods. We show that carefully choosing the granularity parameter can, in some cases, make a substantial difference when trying to realize lower buffer losses or a high channel utilization. Optimal values of the granularity parameter are shown to be closely related to the optical burst length distribution.

We present a detailed analysis of the loss performance in an optical buffer having access to a single outgoing channel. Such a system - consisting of a number of fiber delay lines - differs significantly from a conventional electronic buffer, in that only a discrete set of delays can be realized for contention resolution. This leads to an underutilization of the channel capacity, which reduces overall performance. Our analysis does not require any special assumptions about the burst- or packet-size distribution, which allows us to study the impact this distribution has on performance. For the important special case of fixed-sized bursts, it reveals, amongst others, that matching fiber delay line length with burst duration is not necessarily the optimal solution in terms of loss performance. It further reveals that, in general, this optimal solution is function not only of burst-size characteristics, but of the offered load as well, making the buffer design process a delicate task.

In this paper, we consider a statistical multiplexer model with infinite buffer capacity and a finite number of independent identical bursty traffic sources. The burstiness of the sources is captured by assuming a mixture of two geometrics for the distribution of the active periods and a geometric distribution for the passive periods of the sources. The queueing performance of the multiplexer is studied in this paper using analytical techniques, which results in closed-form expressions for the mean and the tail distribution of the buffer contents and the packet delay. The results of the study are applied to investigate the influence of the variance of the active periods of the traffic sources on multiplexer performance. It is observed that, for a given "mean burstiness", increasing the variance of the active periods leads to a significant increase of the buffer requirements.>

In this paper we study the delay performance of an ATDM switching element, to which messages composed of a variable number of fixed-length packets arrive via "low-speed" access lines, at the rate of one packet per time slot. More specifically, we analyse the message waiting times and the message delays encountered in this switching element, and compare the results with the case of "fast" access lines, in which all the packets of a message arrive in the same slot. The study is an extension/continuation of previous work, which was mainly concerned with the derivation of buffer occupancies and packet delays.>

A multiserver discrete-time buffer system is studied. Packets arrive in the system according to a general correlated process, which is not further specified. The service times of the packets are of constant length. Explicit expressions are derived for the distribution, the probability generating function, and the mean and variance of the packet delay, in terms of the distribution, the probability generating function, and the mean and variance of the buffer contents. It is observed that knowledge of the exact nature of the arrival process is not required to be able to derive these relationships between the statistics of the delay and the occupancy.>

To validate models of sheet metal forming processes, experiments with sheets of metal marked with grids are performed. A method for measuring the deformed grid after processing is presented. It is based on morphological image processing and it requires four steps. A large top hat transformation is first applied to homogenize the grey level intensities of the background. The two main directions of the grid are then determined by calculating covariances. Linear filtering along the directions of the grid is used to extract a mask of the grid pattern. This mask is then skeletonized in order to extract the medial axis of the grid as well as its intersection points.>

A slotted statistical multiplexer with a finite number of input links is considered. Messages arriving on each input link contain a fixed number of fixed-length packets and are carried to the multiplexer in the form of a packet train at the rate of one packet per slot. Several messages may arrive contiguously on an input link; idle periods are geometrically distributed. The multiplexer buffer is modeled as a discrete-time single-server queuing system with train arrivals. By means of a generating function approach, a technique to derive the moments of the buffer occupancy is developed, and an explicit expression for the mean buffer occupancy is given. Furthermore, an approximate method is presented to obtain a tight upper bound for the tail distribution of the buffer occupancy, especially for large traffic load.>

The author considers an asynchronous time-division-multiplexing system with a finite number of identical users generating data only during their so-called active periods, which alternate with so-called passive periods. Assuming geometric distributions for the active and passive periods of the users, the author derives a functional equation which describes the full steady-state buffer behavior of the multiplexer. The buffer occupancy at various moments can be derived from this equation and explicit functions of the parameters of the system. The results indicate a strong dependency of the mean buffer occupancy on the actual lengths of the active and passive periods of the users, even for a given mean user activity.>

A discrete buffered system with infinite buffer size, one single output channel, and periodic opportunities for service (synchronous transmission) is considered in a two-state environment. The output channel is subjected to a random interruption process, which is characterized by a Bernoulli sequence of independent random variables, with probabilities dependent on the environment state. The environment states have random sojourn times with "mixture of geometrics"-type distributions. The arrival process is dependent on the environment state, but arbitrary. For this system, expressions are derived for the probability generating functions of the number of messages in the buffer at various time instants. A number of special cases and possible applications of the model are discussed, and an extended example is given as an illustration of the study.

In a recent paper [1], Ko and Davis have considered the problem of deriving the exact message delay for TDMA channels with multiple contiguous output. Their analysis yields an expression for the average message delay, under the assumption of a Poisson message arrival process. In the present paper a much more general treatment of the same problem is presented, resulting in a closed form expression for the whole probability generating function of the message delay, which is valid for a general arrival process.

The paper considers a class of continuous ARQ strategies, whereby multiple copies of each data block are sent contiguously (instead of one single copy), and whereby the data blocks are delivered at the receiver side in their order of arrival at the transmitter. In order to achieve the best possible throughput efficiency-within this class-an optimum value for the number of copies to be sent is determined, in terms of the block error probability and the propagation delay. It turns out that, depending on these parameters, the optimum scheme is one of the two following alternatives: 1) sending each data block repeatedly until a positive acknowledgment is received for it; 2) sending each block a constant (optimum) number of times. A throughput comparison of the optimum scheme with other related ARQ strategies is given.

This paper deals with a generalized stop-and-wait ARQ scheme, whereby data blocks are sent to the receiver in sets containing an arbitrary number of identical copies. The main idea behind this scheme is a reduction of the idle time of the transmitter.

In the paper Bharath-Kumar presented an analysis of a discrete buffered system of infinite capacity, where the length of the packets is drawn from a geometric distribution and the packets leaving the resource have to be retransmitted with some probability. In this correspondence an analysis of the same system is given which applies for a general packet length distribution, and where the length of a packet remains the same each time it is retransmitted, as opposed to Bharath-Kumar's model where the retransmission packet lengths are independently chosen.