相关论文: Stochastic inequalities for single-server loss que…

With the maturity of web services, containers, and cloud computing technologies, large services in traditional systems (e.g. the computation services of machine learning and artificial intelligence) are gradually being broken down into many…

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

We examine a generalised queuing model which we call the G/G/n/G/+ model, which encompasses the G/G/n and G/G/n/s models as special cases. Our model accommodates useful generalisations in user behaviour and limitations on the facilities for…

Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is…

The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters…

This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…

We discuss weak convergence of the number of busy servers in a $G/G/\infty$ queue in the $J_1$-topology on the Skorokhod space. We prove two functional limit theorems, with random and nonrandom centering, respectively, thereby solving two…

We consider an M/M/1 queueing model where customers can strategically decide to enter or leave the queue. We characterize the class of queueing regimes such that, for any parameters of the model, the socially efficient behavior is an…

In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing…

In this paper, we consider the M/GI/1 queue with single vacations under the gated service discipline. We obtain the probability generating function of the stationary queue length, the Laplace-Stieltjes transform of the system delay…

Use-case-specific network slicing in decentralized multi-tenancy cloud environments is a promising approach to bridge the gap between the demand and supply of resources in next-generation communication networks. Our findings associate…

This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting…

We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model document transfer in a communication network where the documents transferred have a general…

Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered.…

New recursive equations designed for the G/G/m queue are presented. These equations describe the queue in terms of recursions for the arrival and departure times of customers, and involve only the operations of maximum, minimum and…

Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…

This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters.…

Multi-server queueing systems are widely used models for job scheduling in machine learning, wireless networks, crowdsourcing, and healthcare systems. This paper considers a multi-server system with multiple servers and multiple types of…

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…