相关论文: Simple proof of Dynkin's formula for single-server…
Polynomial convergence rates in total variation are established in Erlang-Sevastyanov's type problem with an infinite number of servers and a general distribution of service under assumptions on the intensity of serving.
Recurrence and ergodic properties are established for a single--server queueing system with variable intensities of arrivals and service. Convergence to stationarity is also interpreted in terms of reliability theory.
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…
This paper purpose is to investigate exponential behavior conditions for the infinite servers queue with Poisson arrivals busy period length distribution. It is presented a general theoretical result that is the basis of this work. The…
The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the intensity of the service depend on the state…
We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple input…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a…
A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there…
Polynomial convergence rate to stationarity is shown for extended Erlang -- Sevastyanov's model.
The blocking probability of a finite-source bufferless queue is a fixed point of the Engset formula, for which we prove existence and uniqueness. Numerically, the literature suggests a fixed point iteration. We show that such an iteration…
We obtain a verification theorem for solving a Dynkin game driven by a L\'evy process. The result requires finding two averaging functions that, composed respectively with the supremum and the infimum of the process, summed, and taked the…
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…
This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regime$\unicode{x2014}$where the number of jobs and single-server service rates…
This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…
Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…