Related papers: $M|G|\infty$ Queue Busy Cycle Renewal Function
Two of the most popular approximations for the distribution of the steady-state waiting time, $W_{\infty}$, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic…
Considering the widespread use of effective capacity in cross-layer design and the extensive existence of renewal service processes in communication networks, this paper thoroughly investigates the effective capacity for renewal processes.…
We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…
Accurate parametrization of galaxies detected in the 21-cm HI emission is of fundamental importance to the measurement of commonly used indicators of galaxy evolution, including the Tully-Fisher relation and the HI mass function. Here, we…
We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the…
In queueing systems, effective scheduling algorithms are essential for optimizing performance. Optimal scheduling for the M/G/k queue has been explored in the heavy traffic limit, but much remains unknown in the intermediate load regime. In…
This paper considers a multichannel preemptive-resume priority queueing system with a Poisson input and an arbitrary service time distribution depending on the priority of job. Jobs of the same priority are serviced according to the LIFO…
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 the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…
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…
We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at…
In this work the asymptotic properties of $Q_t(N)$ ,the probability of the number of renewals ($N$), that occur during time $t$ are explored. While the forms of the distribution at very long times, i.e. $t\to\infty$, are very well known and…
The ageing intensity function is a powerful analytical tool that provides valuable insights into the ageing process across diverse domains such as reliability engineering, actuarial science, and healthcare. Its applications continue to…
We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate…
We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'{e}vy process $Y(t)$ which is reflected at 0. When the exponential clock…
This paper investigates the capacity of a channel in which information is conveyed by the timing of consecutive packets passing through a queue with independent and identically distributed service times. Such timing channels are commonly…
We introduce and study some queueing models with random resetting, including Markovian and non--Markovian models. The Markovian models include M/M/$\infty$, M/M/r and M/M/1+M queues with random resetting, in which a continuous-time Markov…
A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…
We improve the accuracy of Active Volume resource estimates by explicitly scheduling when Active Volume blocks execute. We present software that uses a greedy strategy to assign each logical qubit a role in each logical cycle (e.g.,…
Upper and lower class functions for the maximum likelihood estimator of the arrival and the service rates in a $GI/G/1$ queue are studied and the results are verified for M/M/1 queue.