Related papers: Exact Solutions for M/M/c/Setup Queues
Power grid load scheduling is a critical task that ensures the balance between electricity generation and consumption while minimizing operational costs and maintaining grid stability. Traditional optimization methods often struggle with…
A renewal system divides the slotted timeline into back to back time periods called renewal frames. At the beginning of each frame, it chooses a policy from a set of options for that frame. The policy determines the duration of the frame,…
Configuring a storage system to better serve an application is a challenging task complicated by a multidimensional, discrete configuration space and the high cost of space exploration (e.g., by running the application with different…
In this note we consider M/D/1/N queue with renovation and derive analytic expressions for the following performance characteristics: stationary loss rate, moments of the number in the system. Moments of consecutive losses, waiting/sojourn…
Placing applications in mobile edge computing servers presents a complex challenge involving many servers, users, and their requests. Existing algorithms take a long time to solve high-dimensional problems with significant uncertainty…
In this paper we study a periodic-review single-commodity setup-cost inventory model with backorders and holding/backlog costs satisfying quasiconvexity assumptions. We show that the Markov decision process for this inventory model…
The exponential growth of Internet of Things (IoT) devices, smart vehicles, and latency-sensitive applications has created an urgent demand for efficient distributed computing paradigms. Multi-Fog Computing (MFC), as an extension of fog and…
Recommender systems aim to recommend the most suitable items to users from a large number of candidates. Their computation cost grows as the number of user requests and the complexity of services (or models) increases. Under the limitation…
Completeness of a dynamic priority scheduling scheme is of fundamental importance for the optimal control of queues in areas as diverse as computer communications, communication networks, supply chains and manufacturing systems. Our first…
Designing and implementing efficient parallel priority schedulers is an active research area. An intriguing proposed design is the Multi-Queue: given $n$ threads and $m\ge n$ distinct priority queues, task insertions are performed uniformly…
We present in this paper a generic framework for the analysis of multi-threaded programs with recursive procedure calls, synchronisation by rendez-vous between parallel threads, and dynamic creation of new threads. To this end, we consider…
In hybrid Model Predictive Control (MPC), a Mixed-Integer Quadratic Program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC we expect…
Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is…
The maximum possible throughput (or the rate of job completion) of a multi-server system is typically the sum of the service rates of individual servers. Recent work shows that launching multiple replicas of a job and canceling them as soon…
The problem of designing a rebalancing algorithm for a large-scale ridehailing system with asymmetric demand is considered here. We pose the rebalancing problem within a semi Markov decision problem (SMDP) framework with closed queues of…
We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types…
A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential…
We study a continuous-time, infinite-horizon dynamic bipartite matching problem. Suppliers arrive according to a Poisson process; while waiting, they may abandon the queue at a uniform rate. Customers on the other hand must be matched upon…
The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…
In this paper, we study Markov-dependent reflected autoregressive processes, and other related models the analysis of which results in a vector-valued fixed-point functional equation of a certain type. In queueing terms, such processes…