The preemptive repeat hybrid server interruption model

We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline

The distributional form of Little's Law and the Fuhrmann-Cooper decomposition

Includes bibliographical references (p. 15).by J. Keilson and L.D. Servi

Parallelising reception and transmission in queues of secondary users

In a cognitive radio network, the secondary users place the packets to be transmitted on a queue to control the order of arrival and to adapt to the network state. Previous conceptionsassigned to each secondary user a single queue that contains both received and forwarded packets. Our present article divides the main queue into two sub queues: one to receive the arrived packets and the other to transmit the available packets. This approach reduces the transmission delay due on the one hand; to the shifting of data placed on the single queue, and on the other hand; to the sequential processing of reception and transmission, in theprevious designs. All without increasing the memory capacity of the queue, in the new approach

A Generalization of M/G/1 Priority Models via Accumulating Priority

Priority queueing systems are oftentimes set up so that arriving customers are placed into one of $N$ distinct priority classes. Moreover, to determine the order of service, each customer (upon arriving to the system) is assigned a priority level that is unique to the class to which it belongs. In static priority queues, the priority level of a class-$k$ ($k=1,2,\ldots,N$) customer is assumed to be constant with respect to time. This simple prioritization structure is easy to implement in practice, and as such, various types of static priority queues have been analyzed and subsequently applied to real-life queueing systems. However, the assumption of constant priority levels for the customers may not always be appropriate. Furthermore, static priority queues can often display poor system performance as their design does not provide systems managers the means to balance the classical trade-off inherent in all priority queues, that is: reducing wait times of higher priority customers consequently increases the wait times for those of lower priority. An alternative to static priority queues are accumulating priority queues, where the priority level of a class-$k$ customer is assumed to accumulate linearly at rate $b_k>0$ throughout the class-$k$ customer's time in the system. The main benefit of accumulating priority queues is the ability, through the specification of the accumulating priority rates $\{b_k\}_{k=1}^N$, to control the waiting times of each class. In the past, due to the complex nature of the accumulating prioritization structure, the control of waiting times in accumulating priority queues was limited --- being administered only through their first moments. Nowadays, with the advent of a very useful tool called the maximal priority process, it is possible to characterize the waiting time distributions of several types of accumulating priority queues. In this thesis, we incorporate the concept of accumulating priority to several previously analyzed static priority queues, and use the maximal priority process to establish the corresponding steady-state waiting time distributions. In addition, since static priority queues may be captured from accumulating priority queues, useful comparisons between the considered accumulating priority queues and their static priority counterparts are made throughout this thesis. Thus, in the end, this thesis results in a set of extensive analyses on these highly flexible accumulating priority queueing models that provide a better understanding of their overall behaviour, as well as exemplify their many advantages over their static priority equivalents

Strategic behavior and revenue management of cloud services with reservation-based preemption of customer instances

Cloud computing is a multi billion dollar industry, based around outsourcing the provisioning and maintenance of computing resources. In particular, Infrastructure as a Service (IaaS) enables customers to purchase virtual machines in order to run arbitrary software. IaaS customers are given the option to purchase priority access, while providers choose whether customers are preempted based on priority level. The customer decision is based on their tolerance for preemption. However, this decision is a reaction to the provider choice of preemption policy and cost to purchase priority. In this work, a non-cooperative game is developed for an IaaS system offering resource reservations. An unobservable $M|G|1$ queue with priorities is used to model customer arrivals and service. Customers receive a potential priority from the provider, and choose between purchasing a reservation for that priority and accepting the lowest priority for no additional cost. Customers select the option which minimizes their total cost of waiting. This decision is based purely on statistics, as customers cannot communicate with each other. This work presents the impact of the provider preemption policy choice on the cost customers will pay for a reserved instance. A provider may implement a policy in which no customers are preempted (NP); a policy in which all customers are subject to preemption (PR); or a policy in which only the customers not making reservations are subject to preemption (HPR). It is shown that only the service load impacts the equilibrium possibilities in the NP and PR policies, but that the service variance is also a factor under the HPR policy. These factors impact the equilibrium possibilities associated to a given reservation cost. This work shows that the cost leading to a given equilibrium is greater under the HPR policy than under the NP or PR policies, implying greater incentive to purchase reservations. From this it is proven that a provider maximizes their potential revenue from customer reservations under an HPR policy. It is shown that this holds in general and under the constraint that the reservation cost must correspond to a unique equilibrium.2020-06-03T00:00:00

Performance Analysis of Two Priority Queuing Systems in Tandem

In this paper, we consider a tandem of two head-of-line (HOL) non-preemptive priority queuing systems, each with a single server and a deterministic service-time. Two classes of traffic are considered, namely high priority and low priority traffic. By means of a generating function approach, we present a technique to derive closed-form expressions for the mean buffer occupancy at each node and mean delay. Finally, we illustrate our solution technique with some numerical examples, whereby we illustrate the starvation impact of the HOL priority scheduling discipline on the performance of the low-priority traffic stream. Our research highlights the important fact that the unfairness of the HOL priority scheduling becomes even more noticeable at the network level. Thus this priority mechanism should be used with caution

Waiting Time Distributions in the Preemptive Accumulating Priority Queue

The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-015-9476-1We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.Natural Sciences and Engineering Research Council of Canada Discovery Grants program || RGPIN/238675-201

Scheduling, Characterization and Prediction of HPC Workloads for Distributed Computing Environments

As High Performance Computing (HPC) has grown considerably and is expected to grow even more, effective resource management for distributed computing sys- tems is motivated more than ever. As the computational workloads grow in quantity, it is becoming more crucial to apply efficient resource management and workload scheduling to use resources efficiently while keeping the computational performance reasonably good. The problem of efficiently scheduling workloads on resources while meeting performance standards is hard. Additionally, non-clairvoyance of job dimen- sions makes resource management even harder in real-world scenarios. Our research methodology investigates the scheduling problem compliant for HPC and researches the challenges for deploying the scheduling in real world-scenarios using state of the art machine learning and data science techniques.To this end, this Ph.D. dissertation makes the following core contributions: a) We perform a theoretical analysis of space-sharing, non-preemptive scheduling: we studied this scheduling problem and proposed scheduling algorithms with polyno- mial computation time. We also proved constant upper-bounds for the performance of these algorithms. b) We studied the sensitivity of scheduling algorithms to the accuracy of runtime and devised a meta-learning approach to estimate prediction accuracy for newly submitted jobs to the HPC system. c) We studied the runtime prediction problem for HPC applications. For this purpose, we studied the distri- bution of available public workloads and proposed two different solutions that can predict multi-modal distributions: switching state-space models and Mixture Density Networks. d) We studied the effectiveness of recent recurrent neural network models for CPU usage trace prediction for individual VM traces as well as aggregate CPU usage traces. In this dissertation, we explore solutions to improve the performance of scheduling workloads on distributed systems.We begin by looking at the problem from the theoretical perspective. Modeling the problem mathematically, we first propose a scheduling algorithm that finds a constant approximation of the optimal solution for the problem in polynomial time. We prove that the performance of the algorithm (average completion time is the constant approximation of the performance of the optimal scheduling. We next look at the problem in real-world scenarios. Considering High-Performance Computing (HPC) workload computing environments as the most similar real-world equivalent of our mathematical model, we explore the problem of predicting application runtime. We propose an algorithm to handle the existing uncertainties in the real world and show-case our algorithm with demonstrative effectiveness in terms of response time and resource utilization. After looking at the uncertainty problem, we focus on trying to improve the accuracy of existing prediction approaches for HPC application runtime. We propose two solutions, one based on Kalman filters and one based on deep density mixture networks. We showcase the effectiveness of our prediction approaches by comparing with previous prediction approaches in terms of prediction accuracy and impact on improving scheduling performance. In the end, we focus on predicting resource usage for individual applications during their execution. We explore the application of recurrent neural networks for predicting resource usage of applications deployed on individual virtual machines. To validate our proposed models and solutions, we performed extensive trace-driven simulation and measured the effectiveness of our approaches

A Stochastic Product Priority Optimization Method for Remanufacturing System Based on Genetic Algorithm

Increasing number of manufacturers are developing remanufacturing facilities to recover end-of-life products for product/component reuse and material recycling while the high uncertainty pattern of returned products complicates the production planning. In this thesis a stochastic production priority optimization method, considering various priority concerns for remanufacturing systems is developed. Priority ranking and matching algorithm is developed to determine the priority rule, using thirteen weighting factors. Queueing models are developed to formulate the objective function, a genetic algorithm is then developed to search optimal solution under different business configurations. Result of this research will provide insights to priority assignment mechanism, which in turn provides support to manufacturers in decision-making in production planning thus improving the performance of remanufacturing systems

Queueing system with vacations after a random amount of work

This paper considers an M/G/1 queue with the following vacation discipline. The server takes a vacation as soon as it has served a certain amount of work since the end of the previous vacation. If the system becomes empty before the server has completed this amount of work, then it stays idle until the next customer arrival and then becomes active again. Such a vacation discipline arises, for example, in the maintenance of production systems, where machines or equipment mainly degrade while being operational. We derive an explicit expression for the distribution of the time it takes until the prespecified amount of work has been served. For the case the total amount of work till vacation is exponentially distributed, we derive the transforms of the steady-state workload at various epochs, busy period, waiting time, sojourn time, and queue length distributions