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The Annals of applied probability, ISSN 1050-5164, 2/2003, Volume 13, Issue 1, pp. 37 - 53
We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We... 
Integers | Logical proofs | Random walk | Stochastic processes | Random variables | Indicator functions | Stopping distances | Distribution functions | Ruin probability | Long-tailed distribution | Subexponential distribution | DISTRIBUTIONS | STATISTICS & PROBABILITY | ruin probability | long-tailed distribution | subexponential distribution | 60K30 | 60G70 | 60K25
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2010, Volume 47, Issue 4, pp. 1048 - 1057
In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized... 
Markov additive process | Fluctuation theory | Lévy process | fluctuation theory | 60K37 | 60K25
Journal Article
Journal of applied probability, ISSN 0021-9002, 06/2008, Volume 45, Issue 2, pp. 297 - 313
We consider a model of random access (slotted-aloha-type) communication networks of general topology. Assuming that network links receive exogenous arrivals of... 
Slotted aloha | Medium access control | Random multiple access | Stability | Queueing network | queueing network | 90B15 | medium access control | slotted aloha | 60K25 | stability | 68M12
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 3/2017, Volume 6, Issue 1, pp. 1 - 11
This paper presents an analysis of a Markovian feedback queueing system with reneging and retention of reneged customers, multiple working vacations and... 
90B22 | Mathematics, general | Mathematics | 68M20 | 60K25
Journal Article
The Annals of applied probability, ISSN 1050-5164, 12/2009, Volume 19, Issue 6, pp. 2211 - 2269
Journal Article
Journal Article
The Annals of applied probability, ISSN 1050-5164, 6/2007, Volume 17, Issue 3, pp. 809 - 839
In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel-Legendre... 
Ergodic theory | Markov processes | Hyperlinks | Coordinate systems | Trajectories | Matrices | Mathematical functions | Random variables | Poisson process | Fairness | Network bandwidth sharing | Ergodicity | Insensitivity | fairness | MODELS | DATA-NETWORKS | STATISTICS & PROBABILITY | insensitivity | ergodicity | network bandwidth sharing | Mathematics - Probability | 90B15 | 68M20 | 60K25
Journal Article
Advances in applied probability, ISSN 0001-8678, 03/2014, Volume 46, Issue 1, pp. 76 - 101
In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching... 
Cyclic polling | Branching process | Multi-stage gated discipline | Busy period moment | Overload | Random fluid limit | busy period moment | 90B22 | random fluid limit | 90B15 | branching process | 60K25 | multi-stage gated discipline | 60F17 | overload
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2010, Volume 47, Issue 4, pp. 1034 - 1047
We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form... 
Markov additive process | Two-sided reflection | Finite buffer | Overflow process | Fluid model | Inverse local time | finite buffer | two-sided reflection | fluid model | overflow process | 60K37 | inverse local time | 60K25 | 60J55
Journal Article
Annals of Operations Research, ISSN 0254-5330, 6/2019, Volume 277, Issue 2, pp. 161 - 196
This paper considers an infinite-buffer batch-service queue with Markovian arrival process, generally distributed and batch-size-dependent service time. We... 
60G02 | Business and Management | Batch-size-dependent | Server content | Multiple roots | Operations Research/Decision Theory | Markovian arrival process | Theory of Computation | 60K25 | Combinatorics | Queue | Time dependence | Bivariate analysis | Roots | Eigenvalues | Markov processes | Queuing theory | Queues | Eigenvectors | Markov analysis | Buffers
Journal Article
Mathematics of operations research, ISSN 1526-5471, 2020
We consider a system of N identical server pools and a single dispatcher where tasks arrive as a Poisson process of rate λ(N). Arriving tasks cannot be queued,... 
load balancing | join the shortest queue | diffussion limit | functional limit theorems | power-of-d scheme | stochastic coupling | fluid limit | many-server asymptotics
Journal Article
Journal of applied probability, ISSN 0021-9002, 03/2014, Volume 51, Issue 1, pp. 136 - 151
Journal Article
The Annals of applied probability, ISSN 1050-5164, 06/2015, Volume 25, Issue 3, pp. 1420 - 1474
We study the G/\mathit{GI}/\infty queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each... 
Queueing | Markov process | central limit theorem | 60K25 | infinite server | 60J25 | 60F05
Journal Article
Annals of Operations Research, ISSN 0254-5330, 12/2016, Volume 247, Issue 1, pp. 193 - 210
In this paper, we are concerned with the analysis of the queue length and waiting time distributions in a batch arrival $$M^X/G/1$$ M X / G / 1 retrial queue.... 
Waiting time distribution | Queue length distribution | Business and Management | Batch arrivals | Retrial queue | Theory of Computation | Operation Research/Decision Theory | 60K25 | Combinatorics
Journal Article
Advances in applied probability, ISSN 0001-8678, 06/2006, Volume 38, Issue 2, pp. 505 - 521
We consider the stability of the longest-queue-first scheduling policy (LQF), a natural and low-complexity scheduling policy, for a generalized switch model.... 
General Applied Probability | Longest-queue-first scheduling | Fluid limit | Second-order condition | Stability | MaxWeight scheduling | Generalized switch | Local fluid limit | Local pooling | Throughput optimality | local fluid limit | 90B15 | local pooling | second-order condition | longest-queue-first scheduling | 60K25 | 60G17 | stability | throughput optimality | fluid limit
Journal Article
Journal of applied probability, ISSN 0021-9002, 06/2011, Volume 48, Issue 2, pp. 435 - 452
We consider several versions of the job assignment problem for an M/M/m queue with servers of different speeds. When there are two classes of customers,... 
Heterogeneous server | Individual and social optimality | Multiserver queue | 60K30 | individual and social optimality | 60K25 | heterogeneous server
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2015, Volume 52, Issue 4, pp. 990 - 1002
In this paper we consider an M/M/c queue modified to allow both mass arrivals when the system is empty and the workload to be removed. Properties of queues... 
Research Papers | Recurrence | Equilibrium distribution | Idle time | M/M/c queue | Queue size | recurrence | idle time | queue size | equilibrium distribution | 60J27 | 60K25 | 60J35
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2015, Volume 52, Issue 4, pp. 941 - 961
In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot... 
Research Papers | Tollbooth tandem queue | 90B22 | departure-delayed customer | departure delay | 60K25
Journal Article
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