Random Deadlines Research Articles

Age of Information for Multicast Transmission With Fixed and Random Deadlines in IoT Systems

In this article, we consider the multicast transmission of a real-time Internet-of-Things (IoT) system, where an access point (AP) transmits timestamped status updates to multiple IoT devices. Different from the existing studies that only considered multicast transmission without deadlines, we enforce a deadline for the service time of each multicast status update, taking into account both the fixed and randomly distributed deadlines. In particular, a status update is dropped when either its deadline expires or it is successfully received by a certain number of IoT devices. Considering deadlines is important for many emerging IoT applications, where the outdated status updates are of no use to IoT devices. We evaluate the timeliness of the status update delivery by applying a recently proposed metric, named the Age of Information (AoI), which is defined as the time elapsed since the generation of the most recently received status update. After deriving the distributions of the service time for all possible reception outcomes at IoT devices, we manage to obtain the closed-form expressions of both the average AoI and the average peak AoI. Simulations validate the performance analysis, which reveals that the multicast transmission with deadlines achieves a lower average AoI than that without deadlines and there exists an optimal value of the deadline that can minimize the average (peak) AoI. Results also show that the fixed and random deadlines have respective advantages in different deadline regimes.

Resource allocation and routing in parallel multi-server queues with abandonments for cloud profit maximization

This paper considers a Markov decision model for profit maximization of a cloud computing service provider catering to customers submitting jobs with firm real-time random deadlines. Customers are charged on a per-job basis, receiving a full refund if deadlines are missed. The service provider leases computing resources from an infrastructure provider in a two-tier scheme: long-term leasing of basic infrastructure, consisting of heterogeneous parallel service nodes, each modeled as a multi-server queue, and short-term leasing of external servers. Given the intractability of computing an optimal dynamic resource allocation and job routing policy, maximizing the long-run average profit rate, the paper addresses the design, implementation and testing of low-complexity heuristics. The policies considered are a static policy given by an optimal Bernoulli splitting, and three dynamic index policies based on different index definitions: individually optimal (IO), policy improvement (PI) and restless bandit (RB) indices. The paper shows how to implement efficiently each such policy, and presents a comprehensive empirical comparison, drawing qualitative insights on their strengths and weaknesses, and benchmarking their performance in an extensive study.

Optimal dynamic pricing for sponsored search advertising

This paper studies a novel posted pricing business model among Asian search engines for selling sponsored positions to advertisers. The unique feature of bump-up process to eliminate unoccupied positions creates quality uncertainty from the advertisers’ viewpoints. We establish the existence of a Markov perfect equilibrium, and characterize the optimal posted prices in this dynamic selling context. We show that creating quality uncertainty unambiguously boosts the search engine’s profitability. Our analysis applies to the cases with random deadlines and finite population of advertisers.

데드라인을 고려하는 효율적인 지능형 로봇 커버리지 알고리즘

이 논문은 지능형 로봇을 위한 새로운 커버리지 알고리즘을 제안한다. 커버리지 알고리즘의 성능을 향상하기 위한 많은 연구들은 전체 커버리지 완료 시간을 최소화하는데 초점을 맞추어왔다. 그러나, 만일 전체 커버리지를 완료하기에 충분한 시간이 없다면, 최적의 경로는 달라질 수 있다. 이러한 문제를 해결하기 위하여 본 논문에서는 MaxCoverage라고 하는 데드라인이 있을 경우에 가능한 많은 면적을 커버하기 위한 새로운 커버리지 알고리즘을 제안한다. MaxCoverage 알고리즘은 이동 경로를 셋 커버 문제를 위한 그리디 알고리즘을 이용하여 결정한다. 실험 결과에 의하면 MaxCoverage 알고리즘은 임의의 데드라인에 대하여 다른 알고리즘들에 비해 향상된 성능을 보여준다. This paper proposes a new coverage algorithm for intelligent robot. Many algorithms for improving the performance of coverage have been focused on minimizing the total coverage completion time. However, if one does not have enough time to finish the whole coverage, the optimal path could be different. To tackle this problem, we propose a new coverage algorithm, which we call MaxCoverage algorithm, for covering maximal area within the deadline. The MaxCoverage algorithm decides the navigation flow by greedy algorithm for Set Covering Problem. The experimental results show that the MaxCoverage algorithm performs better than other algorithms for random deadlines.

Expulsion and scheduling control for multiclass queues with heterogeneous servers

We consider an M/M/2 system with nonidentical servers and multiple classes of customers. Each customer class has its own reward rate and holding cost. We may assign priorities so that high priority customers may preempt lower priority customers on the servers. We give two models for which the optimal admission and scheduling policy for maximizing expected discounted profit is determined by a threshold structure on the number of customers of each type in the system. Surprisingly, the optimal thresholds do not depend on the specific numerical values of the reward rates and holding costs, making them relatively easy to determine in practice. Our results also hold when there is a finite buffer and when customers have independent random deadlines for service completion.

Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

This paper analyzes a scheduling system where a fixed number of nonpreemptive jobs is to be processed on multiple parallel processors with different processing speeds. Each processor has an exponential processing time distribution and the processors are ordered in ascending order of their mean processing times. Each job has its own deadline that is exponentially distributed with rate ß1, independent of the deadlines of other jobs and also independent of job processing times. A job departs the system as soon as either its processing completes or its deadline occurs. We show that there exists a simple threshold strategy that slochastically minimizes the total delay of all jobs. The policy depends on distributions of processing times and deadlines, but is independent of the rate of deadlines. When the rate of the deadline distribution is 0 (no deadlines), the total delay reduces to the flowtime (the sum of completion times of all jobs). If each job has its own probability of being correctly processed, then an extension of this policy stochastically maximizes the total number of correctly processed, nontardy jobs. We discuss possible generalizations and limitations of this result.

Stochastically maximizing the number of successes in a sequential assignment problem

In the classical sequential assignment problem as introduced by Derman et al. (1972) there are n workers who are to be assigned a finite number of sequentially arriving jobs. If a worker of value p is assigned a job of value x the return is px, where we interpret the return as the probability that the given worker correctly completes the given job. The job value is a random value that is observed upon arrival, and jobs must be assigned or rejected when they arrive. Each worker can only do one job. Derman et al. showed that when the objective is to maximize the expected return, i.e., the expected number of correctly completed jobs, the optimal policy is a simple threshold policy, which does not depend on the worker values. Their result was extended by Albright (1974) to allow job arrivals according to a Poisson process and a single random deadline for job completion (which is equivalent to discounting). Righter (1987) further extended the result to permit workers to have independent random deadlines for job completions. Here we show that when there are independent deadlines a simple threshold policy that is independent of the worker values stochastically maximizes the number of correctly completed jobs, and therefore maximizes the expected number of correctly completed jobs. We also show that there is no policy that stochastically maximizes the number of correctly completed jobs when there is a single deadline. However, when there is single deadline and the objective is to maximize the probability that n jobs are done correctly by n workers, then the optimal policy is determined by a single threshold that is independent of n and of the worker values.

Stochastically maximizing the number of successes in a sequential assignment problem

In the classical sequential assignment problem as introduced by Derman et al. (1972) there are n workers who are to be assigned a finite number of sequentially arriving jobs. If a worker of value p is assigned a job of value x the return is px, where we interpret the return as the probability that the given worker correctly completes the given job. The job value is a random value that is observed upon arrival, and jobs must be assigned or rejected when they arrive. Each worker can only do one job. Derman et al. showed that when the objective is to maximize the expected return, i.e., the expected number of correctly completed jobs, the optimal policy is a simple threshold policy, which does not depend on the worker values. Their result was extended by Albright (1974) to allow job arrivals according to a Poisson process and a single random deadline for job completion (which is equivalent to discounting). Righter (1987) further extended the result to permit workers to have independent random deadlines for job completions. Here we show that when there are independent deadlines a simple threshold policy that is independent of the worker values stochastically maximizes the number of correctly completed jobs, and therefore maximizes the expected number of correctly completed jobs. We also show that there is no policy that stochastically maximizes the number of correctly completed jobs when there is a single deadline. However, when there is single deadline and the objective is to maximize the probability that n jobs are done correctly by n workers, then the optimal policy is determined by a single threshold that is independent of n and of the worker values.

The rejection rate for tasks with random arrivals, deadlines, and preemptive scheduling

A means of approximating light-traffic performance of RAD (random-arrivals-with-deadlines) systems for four basic preemptive scheduling policies is presented. The design goal is to keep congestion low enough to make the probability of rejection acceptably small. These designs must have low processor utilization. The study analyzes rejection probabilities at utilizations up to 20% and rejection probabilities up to about 10% for various well-known preemptive scheduling disciplines (shortest job first, earliest due date, and least laxity first), as well as first-come, first-served. Good approximations for the rejection probability and for a number of other properties, such as the distribution of time-to-go at rejection, are found. >

A Resource Allocation Problem in a Random Environment

We consider a resource allocation problem in which various parameters of the model change according to independent random environment Markov processes. There are a finite number of activities that each require a resource, and resources arrive according to a Poisson process. Both activities and resources have values associated with them and the return from allocating a resource to an activity is the product of the activity value and the resource value. Activity values are known ahead of time but the values of resources are independent random variables from a common distribution and are known only after the arrival of the resource. We wish to assign arriving resources to available activities so as to maximize our total expected return. It is assumed that either there is a single random deadline for all activities, which is the same as discounting the returns, or the activities have independent random deadlines. The model has applications to processor scheduling, selling of assets, and kidney allocation for transplant. We consider the effects on the structure of the optimal policy of allowing parameters to be determined by independent Markov processes. In particular, we permit the resource arrival rate, the activity values, the deadline rates, and the variability of the resource distribution to change. We give conditions under which the total optimal expected return is monotone in the states of the Markov processes. We also show that the total optimal return is increasing and convex in the activity values, decreasing and convex in the deadline rates, and increasing if the variability of the distribution of resource values is increasing.

The Stochastic Sequential Assignment Problem With Random Deadlines

Resources are to be allocated sequentially to activities to maximize the total expected return, where the return from an allocation is the product of the value of the resource and the value of the activity. The set of activities and their values are given ahead of time, but the resources arrive according to a Poisson process and their values are independent random variables that are observed upon arrival. It is assumed that either there is a single random deadline for all activities, which is the same as discounting the returns, or the activities have independent random deadlines. The model has applications machine scheduling, packet switching, and kidney allocation for transplant. It is known that the optimal policy in the discounted case has a very simple form that does not depend on the activity values. We show that this is also true when the deadlines are independent and in this case the solution can expressed in terms of solutions to single activity models. These results also hold when there are batch arrivals of resources. The effects of pooling separate identical systems with a single activity into a combined system is investigated for both models. When activities have independent deadlines it is optimal to reject a resource in the combined system if and only if it is optimal to reject it in the single activity system. However, when returns are discounted, it is sometimes optimal to accept a resource in the combined system that would be rejected in the single activity system.