A queue with service interruptions in an alternating random environment
Operations Research
Queues with slowly varying arrival and service processes
Management Science
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
A Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 Queue
Journal of the ACM (JACM)
Calculation of the Steady State Waiting Time Distribution in GI/PH/c and MAP/PH/c Queues
Queueing Systems: Theory and Applications
Asymptotic analysis of the M/G/1 queue with a time-dependent arrival rate
Queueing Systems: Theory and Applications
A single server queue with service interruptions
Queueing Systems: Theory and Applications
An Exact Solution for an M(t)/M(t)/1 Queue with Time-Dependent Arrivals and Service
Queueing Systems: Theory and Applications
Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times
Queueing Systems: Theory and Applications
Sojourn Time Distributions in Modulated G-Queues with Batch Processing
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Queues with system disasters and impatient customers when system is down
Queueing Systems: Theory and Applications
On the inapproximability of M/G/K: why two moments of job size distribution are not enough
Queueing Systems: Theory and Applications
Probabilistic performance modeling of virtualized resource allocation
Proceedings of the 7th international conference on Autonomic computing
Asymptotically Optimal Controls for Time-Inhomogeneous Networks
SIAM Journal on Control and Optimization
Throughput-smoothness tradeoff in preventing competing TCP from starvation
Computer Communications
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Systems whose arrival or service rates fluctuate over time are very common, but are still not well understood analytically. Stationary formulas are poor predictors of systems with fluctuating load. When the arrival and service processes fluctuate in a Markovian manner, computational methods, such as Matrix-analytic and spectral analysis, have been instrumental in the numerical evaluation of quantities like mean response time. However, such computational tools provide only limited insight into the functional behavior of the system with respect to its primitive input parameters: the arrival rates, service rates, and rate of fluctuation.For example, the shape of the function that maps rate of fluctuation to mean response time is not well understood, even for an M/M/1 system. Is this function increasing, decreasing, monotonic? How is its shape affected by the primitive input parameters? Is there a simple closed-form approximation for the shape of this curve? Turning to user experience: How is the performance experienced by a user arriving into a "high load" period different from that of a user arriving into a "low load" period, or simply a random user. Are there stochastic relations between these? In this paper, we provide the first answers to these fundamental questions.