Tail behaviour of the area under the queue length process of the single server queue with regularly varying service times

DOI10.1007/s11134-005-0926-2zbMath1077.60519OpenAlexW2127807461MaRDI QIDQ2572912

Zbigniew Palmowski, Rafał Kulik

Publication date: 7 November 2005

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11134-005-0926-2

zbMATH Keywords

busy periodsubexponential distributiontotal workload

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (2)

Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations ⋮ A Note on Skewness in Regenerative Simulation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the area swept under the occupation process of an \(M/M/1\) queue in a busy period
• Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and first passage probabilities
• Extreme value theory for queues via cycle maxima
• Asymptotics for M/G/1 low-priority waiting-time tail probabilities
• Stopped two-dimensional perturbed random walks and Lévy processes
• Large deviations results for subexponential tails, with applications to insurance risk
• Patterns of buffer overflow in a class of queues with long memory in the input stream
• Sampling at subexponential times, with queueing applications
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift.
• Tail asymptotics for M/G/1 type queueing processes with subexponential increments
• Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times
• The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk
• Tail Asymptotics for the Busy Period in the GI/G/1 Queue
• Convergence rates for M/G/1 queues and ruin problems with heavy tails
• On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1
• On the integral of the workload process of the single server queue
• Transient characteristics of an M/M/∞ system
• Integral Limit Theorems Taking Large Deviations into Account when Cramér’s Condition Does Not Hold. I
• The total waiting time in a busy period of a stable single-server queue, I.
• The total waiting time in a busy period of a stable single-server queue, II
• Functional limit theorems for the queue GI/G/1 in light traffic
• Probability Inequalities for Sums of Independent Random Variables
• Large Deviations of Square Root Insensitive Random Sums

This page was built for publication: Tail behaviour of the area under the queue length process of the single server queue with regularly varying service times