Related papers: On {\em BASTA} for Discrete-Time Queues
We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those…
Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a…
In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…
We consider the serve-the-longest-queue discipline for a multiclass queue with buffers of equal size, operating under (i) the conventional and (ii) the Halfin-Whitt heavy traffic regimes, and show that while the queue length process'…
We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and…
Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
In this paper, we propose an ETA model (Estimated Time of Arrival) that leverages an attention mechanism over historical road speed patterns. As autonomous driving and intelligent transportation systems become increasingly prevalent, the…
Statistical static timing analysis (SSTA) is studied from the point of view of mathematical optimization. We present two formulations of the problem of finding the critical path delay distribution that were not known before: (i) a…
Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing…
We study airplane boarding in the limit of large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a 1+1 dimensional space-time with a flat Lorentzian metric. The…
The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares…
We study critical GI/G/1 queues under finite second moment assumptions. We show that the busy period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics…
We study the problem of scheduling delay-sensitive jobs over spot and on-demand cloud instances to minimize average cost while meeting an average delay constraint. Jobs arrive as a general stochastic process, and incur different costs based…
Time-dependent driving holds the promise of realizing dynamical phenomenon absent in static systems. Here, we introduce a correlated random driving protocol to realize a spatiotemporal order that cannot be achieved even by periodic driving,…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems,…
Polling systems have been widely studied, however most of these studies focus on polling systems with renewal processes for arrivals and random variables for service times. There is a need driven by practical applications to study polling…
In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…
A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival and service time distributions. We address this extremal queue problem by…