Queues with service times and interarrival times depending linearly and randomly upon waiting times

DOI10.1007/BF02411482zbMath0707.60090MaRDI QIDQ919730

Ward Whitt

Publication date: 1990

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

zbMATH Keywords

stationaryergodicStability criteriabranching processes in a random environmentproblem of scheduling interarrival timessteady-state limit

Mathematics Subject Classification ID

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

Related Items (18)

Service Systems with Slowdowns: Potential Failures and Proposed Solutions ⋮ When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence ⋮ On optimization of stochastic max-min-plus-scaling systems -- an approximation approach ⋮ On a modified version of the Lindley recursion ⋮ On moment stability properties for a class of state-dependent stochastic networks ⋮ On queues with service and interarrival times depending on waiting times ⋮ Tail Asymptotics for a Random Sign Lindley Recursion ⋮ Stationary waiting time derivatives ⋮ Stability analysis of a general state-dependent multiserver queue ⋮ Queues with waiting time dependent service ⋮ \(V\)-uniform ergodicity for state-dependent single class queueing networks ⋮ M/G/\(1\) queue with event-dependent arrival rates ⋮ A multiplicative version of the Lindley recursion ⋮ Non-Markovian State-Dependent Networks in Critical Loading ⋮ An \(M/M/c\) queue with queueing-time dependent service rates ⋮ DYNAMIC CONTROL OF A SINGLE-SERVER SYSTEM WHEN JOBS CHANGE STATUS ⋮ On Whitt's conjecture for queues in which service times and interarrival times depend linearly and randomly upon waiting times ⋮ When to Use Speedup: An Examination of Service Systems with Returns

Cites Work

• On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
• Single-Server with Delay-Dependent Arrival Streams
• The stochastic equation Y_n+1=A_nY_n + B_n with stationary coefficients
• Some Useful Functions for Functional Limit Theorems
• A method for solving a class of recursive stochastic equations
• On the heavy-traffic limit theorem for GI/G/∞ queues
• Techniques for establishing ergodic and recurrence properties of continuous-valued markov chains
• Single-Server Queues with Service Time Dependent on Waiting Time
• Queues with State-Dependent Stochastic Service Rates
• Some Results for Bulk-Arrival Queues with State-Dependent Service Times
• Stochastic Abelian and Tauberian theorems
• A queue with waiting time dependent service times
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