相关论文: Losses in M/GI/m/n Queues
What determines the average length of a queue which stretches in front of a service station? The answer to this question clearly depends on the average rate at which jobs arrive at the queue and on the average rate of service. Somewhat less…
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…
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…
A two-sided matching system is considered, where servers are assumed to arrive at a fixed rate, while the arrival rate of customers is modulated via a price-control mechanism. We analyse a loss model, wherein customers who are not served…
In many systems, servers do not turn on instantly; instead, a setup time must pass before a server can begin work. These "setup times" can wreak havoc on a system's queueing; this is especially true in modern systems, where servers are…
We consider the problem of customer equilibrium behavior of a single server Markovian queue with dynamic control of the service rate. Customers arrive according a Poisson procedure and the system administrator makes a service rate choice…
In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical…
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…
Given the busy period and busy cycle major importance in queuing systems, it is crucial the knowledge of the respective distribution functions that is what allows the calculation of the important probabilities. For the M|G|$\infty$ queue…
The models studied in the steady state involve two queues which are served either by a single server whose speed depends on the number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
In discrete time, customers arrive at random. Each waits until one of two servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. In the context of an emergency room (for…
We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…
In this paper we investigate an M/M/$\infty$ queue whose parameters depend on an external random environment that we assume to be a semi-Markovian process with finite state space. For this model we show a recursive formula that allows to…
We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an $M^{X}/G/1$ queue. Once the number of customers in the working mode drops…
Motivated by call center practice, we propose a tractable model for $\mbox{GI}/\mbox{GI}/n+\mbox{GI}$ queues in the efficiency-driven (ED) regime. We use a one-dimensional diffusion process to approximate the virtual waiting time process…
We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal…