Related papers: M|D|$\infty$ Queue Busy Period and Busy Cycle Dist…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in…
We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…
S. G. Kou and H. Wang [First Passage times of a Jump Diffusion Process \textit{Ann. Appl. Probab.} {\bf 35} (2003) 504--531] give expressions of both the (real) Laplace transform of the distribution of first passage time and the (real)…
In high performance computing, scheduling of tasks and allocation to machines is very critical especially when we are dealing with heterogeneous execution costs. Simulations can be performed with a large variety of environments and…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
Round Robin (RR) scheduling algorithm is a preemptive scheduling algorithm. It is designed especially for time sharing Operating System (OS). In RR scheduling algorithm the CPU switches between the processes when the static Time Quantum…
In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in…
Round Robin (RR) Scheduling is the basis of time sharing environment. It is the combination of First Come First Served (FCFS) scheduling algorithm and preemption among processes. It is basically used in a time sharing operating system. It…
Markov decision processes (MDPs) are a popular model for decision-making in the presence of uncertainty. The conventional view of MDPs in verification treats them as state transformers with probabilities defined over sequences of states and…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
Timely and efficient dissemination of server status is critical in compute-first networking systems, where user tasks arrive dynamically and computing resources are limited and stochastic. In such systems, the access point plays a key role…
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…
Present-day quantum systems face critical bottlenecks, including limited qubit counts, brief coherence intervals, and high susceptibility to errors-all of which obstruct the execution of large and complex circuits. The advancement of…
Scheduling is the central concept used frequently in Operating System. It helps in choosing the processes for execution. Round Robin (RR) is one of the most widely used CPU scheduling algorithm. But, its performance degrades with respect to…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage…
A key operational challenge for call centers is to decide, in real time, which waiting customer should be served by which available agent. This is known as skill-based routing, and the decision becomes especially difficult in large systems…