In optical packet/burst switched networks fiber loops provide a viable and compact means of contention resolution. For fixed size packets it is known that a basic void-avoiding schedule (VAS) can vastly outperform a more classical pre-reservation algorithm as FCFS. For the setting of a uniform distributed packet size and a restricted buffer size we proposed two novel forward-looking algorithms, WAS and XAS, that, in specific settings, outperform VAS up to 20% in terms of packet loss. This contribution extends the usage and improves the performance of the WAS and XAS algorithms by introducing an additional threshold variable. By optimizing this threshold, the process of selectively delaying packet longer than strictly necessary can be made more or less strict and as such be fitted to each setting. By Monte Carlo simulation it is shown that the resulting T-WAS and T-XAS algorithms are most effective for those instances where the algorithms without threshold can offer no or only limited performance improvement.

With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines (for delay assignments) and wavelength conversion (for channel assignments) are used to avoid contention between contending packets. The involved scheduling algorithms decide on which Fiber Delay Line and wavelength each packet is scheduled in order to maximize performance. For the setting without wavelength conversion we proposed a scheduling algorithm for assigning delays called void-creating algorithm that outperforms existing void filling algorithms for a variety of packet size distributions. This is achieved by selectively delaying packets longer than strictly necessary based on a numerical procedure that assigns a theoretical value to each void based on how likely the void will eventually be filled and thus prove useful. This contribution extends the concept of void-creation to the important case with multiple wavelengths, where also the channel has to be assigned. Results obtained by Monte Carlo simulation show that with our void-creating algorithm the obtainable improvement in various performance measures highly depends on the number of wavelengths present.

In optical packet/burst switched networks fiber loops provide a viable and compact means of contention resolution. For fixed size packets it is known that a basic void-avoiding schedule (VAS) can vastly outperform a more classical pre-reservation algorithm as FCFS. In this contribution we propose two novel forward-looking algorithms, WAS and XAS, that outperform VAS in the setting of a uniform distributed packet size and a restricted buffer size. This paper presents results obtained by Monte Carlo simulation, showing that improvements of more than 20% in packet loss in specific settings are obtainable. In other settings and for other performance measures similar improvements are within reach.

Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we first study a basic case and then subsequently incorporate the concepts of a setup time and a deactivation time in extended versions of the model. In all cases, we obtain a full characterization of the stationary queue length distribution. This allows us to evaluate the performance in terms of the mentioned balance between performance and energy, using an existing cost function as well as a newly proposed variant thereof. This paper presents the derivation of the stationary distribution as well as several numerical examples of the cost-based performance evaluation.

In optical packet/burst switching, fibre-loop optical buffers provide a compact and effective means of contention resolution. In case of a fixed packet length, the involved loop length is typically chosen matched (equal to the packet length), and the loops are arranged in parallel, constituting a single-stage buffer. In this contribution, we investigate the performance of such a buffer in an asynchronous network setting, assuming (batch-)Poisson arrivals and assuming a so-called void-avoiding schedule (VAS). We show that by time discretisation, the fibre-loop system behaviour can be captured by a particular type of exhaustive polling model. Performance measures such as the moments of the queue content and packet delay for the discretised as well as for the asynchronous optical buffer model are obtained. We illustrate our approach by various numerical examples obtain several insights, including the contra-intuitive finding that under the VAS, both the standard deviation and the coefficient of variation of the queue content are lower than under other regular scheduling disciplines.

Recently, queues with speed scaling have received considerable attention due to their applicability to data centers, enabling a better balance between performance and energy consumption. This paper proposes a new model where blocked customers must leave the service area and retry after a random time, with retrial rate either varying proportionally to the number of retrying customers (linear retrial rate) or non-varying (constant retrial rate). For both, we study the case without and with setup time. In all four cases, we obtain an exact solution for the stationary queue length distribution. This document presents the resulting expressions as well as their derivation.

With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines are used to avoid contention between packets on a single wavelength. The involved scheduling algorithms decide on which Fiber Delay Line each packet is scheduled in order to maximize performance. By selectively delaying packets longer than strictly necessary, we proposed a schedule called void-creation that outperforms existing void-filling algorithms by up to 50 % for a specific setting with fixed packet size. This contribution extends the concept of void-creation to the case of variable size packets. By conditioning the theoretical value of the packet size on the scheduling parameters, we are able to extend the applicability of the void-creating algorithm to a plurality of settings. We therefore developed a numerical procedure that assigns a theoretical value (or, equivalently, negative cost) to each void based on how likely the void will eventually be filled and thus proven useful. Results obtained by Monte Carlo simulation show that our void-values provide a solid and consistent basis to decide upon void creation, and this for a variety of packet size distributions.

This letter focuses on the waiting time of customers in a single-server queueing system, served according to one of two well-known scheduling disciplines, Random-Order-of-Service (ROS) and First-Come-First-Served (FCFS). Arrivals are modeled with a Markov-Modulated Poisson Process (MMPP); service times are exponential. For two basic settings, ROS outperforms FCFS by several percent in terms of mean waiting time. This finding is supported by Monte Carlo simulation, as well as an intuitive argument, motivating the usefulness of ROS as alternative to FCFS.

With ever-increasing demand for bandwidth, optical packet/burst switching is proposed to utilize more of the available capacity of optical networks in the future. In these packet-based switching techniques, packet contention on a single wavelength is resolved effectively by means of Fiber Delay Lines. The involved scheduling algorithms are typically designed to minimize packet loss and/or packet delay. By filling so-called voids, void-filling algorithms are known to outperform their non-void-filling counterparts. This however comes at a large computational cost as the void-filling algorithms have to keep track of beginnings and endings of all voids. This is opposed to the non-void-filling algorithms which only have to keep track of a single system state variable. We therefore propose a new type of algorithm that selectively creates voids that are larger than strictly needed, only when these will likely be filled. Results obtained by Monte Carlo simulation show that selective void creation can jointly reduce packet loss by 50% and packet delay by 18%, without imposing a high computational cost.

As Internet traffic will further increase in coming years, the current optical 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 fibre capacity. To resolve packet contention in the involved optical switches, Fibre 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 in minimizing packet loss 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 for a limited number of wavelength converters 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. The new algorithms are of the same implementation complexity as existing cost-based algorithms, and thus are of immediate value to switch designers. (C) 2015 Elsevier B.V. All rights reserved.

Symbiotic job scheduling exploits the fact that in a system with shared resources, the performance of jobs is impacted by the behavior of other co-running jobs. By coscheduling combinations of jobs that have low interference, the performance of a system can be increased. In this paper, we investigate the impact of using symbiotic job scheduling for increasing throughput. We find that even for a theoretically optimal scheduler, this impact is very low, despite the substantial sensitivity of per job performance to which other jobs are coscheduled: for example, our experiments on a 4-thread SMT processor show that, on average, the job IPC varies by 37% depending on coscheduled jobs, the per-coschedule throughput varies by 69%, and yet the average throughput gain brought by optimal symbiotic scheduling is only 3%. This small margin of improvement can be explained by the observation that all the jobs need to be eventually executed, restricting the job combinations a symbiotic job scheduler can select to optimize throughput. We explain why previous work reported a substantial gain from symbiotic job scheduling, and we find that (only) reporting turnaround time can lead to misleading conclusions. Furthermore, we show how the impact of scheduling can be evaluated in microarchitectural studies, without having to implement a scheduler.

In optical packet/burst switching, fiber delay line (FDL) optical buffers provide an effective means of contention resolution. In many implementations, a single-stage buffer is assumed. In this contribution, however, we analyze a multistage setting, with the second stage consisting of only a single small delay line. For the stability analysis, we take the analysis of a non-equidistant single-stage buffer as a starting point, adding so-called exceptions to cover the two-stage case. Methodologically, we rely on probability generating functions (pgf's).

In optical packet/burst switching, packet contention on a single wavelength is resolved effectively by means of Fiber Delay Lines. The involved scheduling algorithm is typically designed to minimize packet loss, by filling so-called voids, and trying to keep the so-called gaps small. We propose a new type of algorithm that selectively creates voids that are larger than strictly needed, only when these will likely be filled. Results obtained by Monte Carlo simulation show that selective void creation can significantly reduce packet loss.

In operations research and networking problems, random-order-of-service (ROS) provides a well-known alternative to the classic first-come-first-served (FCFS) policy. Models with ROS policy are typically harder to analyze than their FCFS counterparts, with some performance measures notoriously hard to obtain. While significant progress has been realized in the analysis of random-order-of-service models with homogeneous customer service demands, the impact of heterogeneous customer demand is largely unknown. The current contribution studies this impact, with a discrete-time random-order-of-service queue serving customers with heterogeneous demands. Customer service times are independent random variables with type-dependent distribution. The numbers of new arrivals in each slot are independent and identically distributed over time, but can be type-correlated within a single slot. This corresponds to bursty input traffic generated by a finite number of sources, with one source for each type. The burstiness consists in correlation among sources (or types): the rate at which a source generates customers depends on the instantaneous rate of all other sources (and vice versa). Using a transform-based approach yields closed-form formulas for the first few moments of the customer waiting time. Facilitator is a multi-stage description of the customer sojourn, which allows establishing a relation between the so-called conditional waiting time and the actual steady-state customer waiting time. A somewhat unexpected result shows that, under certain conditions on the arrival and service processes, the random-order-of-service policy outperforms the first-come-first-served policy in terms of mean waiting time. A number of numerical examples illustrate this finding.

Symbiotic job scheduling exploits the fact that in a system with shared resources, the performance of jobs is impacted by the behavior of other co-running jobs. By coscheduling combinations of jobs that have low interference, the performance of a system can be increased. In this paper, we investigate the impact of using symbiotic job scheduling for increasing throughput. We find that even for a theoretically optimal scheduler, this impact is very low, despite the substantial sensitivity of per job performance to which other jobs are coscheduled: for example, our experiments on a 4-thread SMT processor show that, on average, the job IPC varies by 37% depending on coscheduled jobs, the per-coschedule throughput varies by 69%, and yet the average throughput gain brought by optimal symbiotic scheduling is only 3%. This small margin of improvement can be explained by the observation that all the jobs need to be eventually executed, restricting the job combinations a symbiotic job scheduler can select to optimize throughput. We explain why previous work reported a substantial gain from symbiotic job scheduling, and we find that (only) reporting turnaround time can lead to misleading conclusions. Furthermore, we show how the impact of scheduling can be evaluated in microarchitectural studies, without having to implement a scheduler.

Running multiple programs on a processor aims at increasing the throughput of that processor. However, defining meaningful throughput metrics in a simulation environment is not as straightforward as reporting execution time. This has led to an ongoing debate on what forms a meaningful throughput metric for multiprogram workloads. We present a method to construct throughput metrics in a systematic way: we start by expressing assumptions on job size, job distribution, scheduling, and so forth that together define a theoretical throughput experiment. The throughput metric is then the average throughput of this experiment. Different assumptions lead to different metrics, so one should be aware of these assumptions when making conclusions based on results using a specific metric. Throughput metrics should always be defined from explicit assumptions, because this leads to a better understanding of the implications and limits of the results obtained with that metric. We elaborate multiple metrics based on different assumptions. In particular, we identify the assumptions that lead to the commonly used weighted speedup and harmonic mean of speedups. Our study clarifies that they are actual throughput metrics, which was recently questioned. We also propose some new throughput metrics, which cannot always be expressed as a closed formula. We use real experimental data to characterize metrics and show how they relate to each other.

In call centers, call blending consists in the mixing of incoming and outgoing call activity, according to some call blending balance. Recently, Artalejo and Phung-Duc have developed an apt model for such a setting, with a two way communication retrial queue. However, by assuming a classical (proportional) retrial rate for the incoming calls, the short-term blending balance is heavily impacted by the number of incoming calls, which may be undesired, especially when the balance between incoming and outgoing calls is vital to the service offered. In this contribution, we consider an alternative to classical call blending, through a retrial queue with constant retrial rate for incoming calls. For the single-server case (one operator), a generating functions approach enables to derive explicit formulas for the joint stationary distribution of the number of incoming calls and the system state, and also for the factorial moments. This is complemented with a stability analysis, expressions for performance measures, and also recursive formulas, allowing reliable numerical calculation. A correlation study enables to study the system’s short-term blending balance, allowing to compare it to that of the system with classical retrial rate. For the multiserver case (multiple operators), we provide a quasi-birth-and-death process formulation, enabling to derive a sufficient and necessary condition for stability in this case (in a simple form), a numerical recipe to obtain the stationary distribution, and a cost model.