Related papers: A large-deviations analysis of the GI/GI/1 SRPT qu…
Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…
We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our main interest is in the quenched and annealed large deviation properties of the last…
Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze…
Motivated by applications in computing and telecommunication systems, we investigate the problem of estimating p-quantile of steady-state sojourn times in a single-server multi-class queueing system with non-preemptive priorities for p…
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…
For a single server system, Shortest Remaining Processing Time (SRPT) is an optimal size-based policy. In this paper, we discuss scheduling a single-server system when exact information about the jobs' processing times is not available.…
In the study of large scale stochastic networks with resource management, differential equations and mean-field limits are two key techniques. Recent research shows that the expected fraction vector (that is, the tailed probability vector)…
In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool,…
Rather than directly considering the queuing delay of data, this memo focuses on reducing the delay that congestion signals experience within a queue management algorithm, which can be greater than the delay that the data itself experiences…
Queue length monitoring is a commonly arising problem in numerous applications such as queue management systems, scheduling, and traffic monitoring. Motivated by such applications, we formulate a queue monitoring problem, where there is a…
We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer…
The increasing use of cloud computing for latency-sensitive applications has sparked renewed interest in providing tight bounds on network tail latency. Achieving this in practice at reasonable network utilization has proved elusive, due to…
We are concerned with an $M/M$-type join the shortest queue ($M/M$-JSQ for short) with $k$ parallel queues for an arbitrary positive integer $k$, where the servers may be heterogeneous. We are interested in the tail asymptotic of the…
We analyze the delay performance of small cell networks operating under random scheduling (RS) and round robin (RR) protocols. Based on stochastic geometry and queuing theory, we derive accurate and tractable expressions for the…
The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…
We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without…
For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system…
Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary…
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…