This paper considers a parallel system of queues fed by independent arrival streams, where the service rate each queue depends on number customers in all queues. Necessary and sufficient conditions for stability are derived, based stochastic monotonicity marginal drift properties multiclass birth death processes. These yield sharp characterization systems, is decreasing other queues, has uniform limits as lengths tend to infinity. The results illustrated with applications region may be nonconvex.

The performance evaluation of wireless networks is severely complicated by the specific features radio communication, such as highly variable channel conditions, interference issues, and possible hand-offs among base stations. latter elements have no natural counterparts in wireline scenarios, create a need for novel models that account impact these characteristics on service rates users. Motivated above we review several characterizing capacity evaluating flow-level carrying elastic data...

We study the time complexity for search of local minima in random graphs whose vertices have i.i.d. cost values. show that, Erdös-Rényi with connection probability given by λ∕nα (with λ > 0 and 0<α<1), a family algorithms that approximate gradient descent find faster than full descent. Furthermore, we probabilistic representation running these leading to asymptotic estimates mean times.

Though very popular, it is well known that the Expectation-Maximisation (EM) algorithm for Gaussian mixture model performs poorly non-Gaussian distributions or in presence of outliers noise. In this paper, we propose a Flexible EM-like Clustering Algorithm (FEMCA): new clustering following an EM procedure designed. It based on both estimations cluster centers and covariances. addition, using semi-parametric paradigm, method estimates unknown scale parameter per data point. This allows to...

We investigate the scheduling of a common resource between several concurrent users when feasible transmission rate each user varies randomly over time. Time is slotted, and arrive depart upon service completion. This may model, for example, flow-level behavior end-users in narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria, we consider stability system mean delay experienced by users. Given complexity problem, fluid-scaled system, which allows to obtain important...

Nous considérons $N$ particules indépendantes. Chaque particule suit l'évolution d'un processus de Galton–Watson sous-critique jusqu'au moment où elle touche $0$. À cet instant, cette choisit uniformément au hasard la position d'une des autres et y saute. Ce est appelé Fleming–Viot. montrons que pour chaque entier $N$, il existe une unique mesure invariante le Fleming–Viot, empirique stationnaire converge vers loi quasi-stationnaire minimale conditionné à ne pas mourir.

A large variety of communication systems, including telephone and data networks, can be represented by so-called Whittle networks. The stationary distribution these networks is insensitive, depending on the service requirements at each node through their mean only. These models are considerable practical interest as derived engineering rules robust to evolution traffic characteristics. In this paper we relax usual assumption static routing address issue dynamic load balancing. Specifically,...

The main motivation to investigate redundancy models comes from empirical evidence suggesting that can help improve the performance of real-world applications. Although there are several variants a redundancy-based system, general notion is create multiple copies same job will be sent subset servers. By allowing for redundant copies, aim minimize system latency by exploiting variability in queue lengths and capacity different In this article, stability condition multiserver systems...

SINDy is a method for learning system of differential equations from data by solving sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)PNASA60027-842410.1073/pnas.1517384113]. In this article, we propose an extension the that learns systems in cases where some variables are not observed. Our based on regressing higher order time derivative target variable onto dictionary functions includes lower derivatives variable. We...

We consider a matching system where items arrive one by at each node of compatibility network according to Poisson processes and depart from it as soon they are matched compatible item. The policy considered is generalized max-weight decisions can be noisy. Additionally, some the nodes may have impatience, that is, leave before being matched. Using specific properties policy, we construct simple quadratic Lyapunov function. This allows us establish stability results, prove exponential...

Channel-aware scheduling strategies provide an effective mechanism for improving the throughput performance in wireless data networks by exploiting channel fluctuations. The of channel-aware algorithms has mainly been examined at packet level a static user population, often assuming infinite backlogs. Recently, some studies have also explored flow-level scenario with dynamics governed arrival and completion random service demands over time. Although certain cases may be evaluated means...

We investigate the stability condition of redundancy-$d$ multi-server systems. Each server has its own queue and implements popular scheduling disciplines such as First-Come-First-Serve (FCFS), Processor Sharing (PS), Random Order Service (ROS). New jobs arrive according to a Poisson process copies each job are sent $d$ servers chosen uniformly at random. The service times assumed be exponentially distributed. A departs soon one finishes service. Under assumption that all i.i.d., we show for...

Several recent experiments have established by measuring the Mandel $Q$ parameter that number of Rydberg excitations in ultracold gases exhibits sub-Poissonian statistics. This effect is attributed to blockade occurs due strong interatomic interactions between highly excited atoms. Because this effect, system can end up a state which all particles are either or blocked: jamming limit. We analyze appropriately constructed random-graph models capture and derive formulae for mean variance...

We study a cloud environment in which computing instances may either be reserved advance, or dynamically spawned to serve fluctuating unknown load. first consider centralized scheme where system operator maintains the job queue and controls spawning of additional capacity; through queueing models their fluid diffusion counterparts we explore tradeoff between delay service capacity variability. Secondly, setting dispatcher who must immediately send jobs, with no delay, decentralized...

A large variety of communication systems, including telephone and data networks, can be represented by so-called Whittle networks. The stationary distribution these networks is insensitive, depending on the service requirements at each node through their mean only. These models are considerable practical interest as derived engineering rules robust to evolution traffic characteristics. In this paper we relax usual assumption static routing address issue dynamic load balancing. Specifically,...

We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing evolution a large class stochastic systems, typical example being randomly varying number flow-level transfers in telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide generic method to construct Lyapunov function when drift is smooth on ℝ N . This approach gives elementary direct proof ergodicity. also...

We analyze the performance of redundancy in a multi-type job and server system where PS is implemented. characterize stability condition, which coincides with that each type only dispatches copies into its least-loaded servers, those need to be fully served. then investigate impact condition by comparing non-redundant arrival routed one randomly selected compatible server. observe if loads are sufficiently heterogeneous can considerably improve region system.

We analyze the performance of redundancy in a multi-type job and server system. assume dispatcher is unaware servers' capacities, we set out to study under which circumstances improves performance. With an arriving dispatches redundant copies all its compatible servers, departs as soon one completes service. As benchmark comparison, take non-redundant system arrival routed only randomly selected server. Service times are generally distributed identical, i.e., have same service requirement....