Markov-modulated queueing systems
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Numerical investigation of a multiserver retrial model
Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
Numerical methods in Markov chain modeling
Operations Research
Inventory control in a fluctuating demand environment
Operations Research
On the M/M/1 Queue with Catastrophes and Its Continuous Approximation
Queueing Systems: Theory and Applications
A Queueing Theory Model of Nonstationary Traffic Flow
Transportation Science
An M/PH/kretrial queue with finite number of sources
Computers and Operations Research
Single-Server Queues with Markov-Modulated Arrivals and Service Speed
Queueing Systems: Theory and Applications
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
QBD approximations of a call center queueing model with general patience distribution
Computers and Operations Research
Decomposition property for markov-modulated queues with applications to warranty management
Probability in the Engineering and Informational Sciences
Cellular mobile networks with repeated calls operating in random environment
Computers and Operations Research
An efficient solution to a retrial queue for the performability evaluation of DHCP
Computers and Operations Research
A matrix continued fraction algorithm for the multiserver repeated order queue
Mathematical and Computer Modelling: An International Journal
A BMAP|PH|1 queue with feedback operating in a random environment
Mathematical and Computer Modelling: An International Journal
A single server priority queue with server failures and queue flushing
Operations Research Letters
Markovian queueing networks in a random environment
Operations Research Letters
A queueing network model with catastrophes and product form solution
Operations Research Letters
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Quasi-birth-and-death processes, that is multi-dimensional Markov chains with block tridiagonal transition probability or generator matrices, are appropriate models for various types of queueing systems, amongst many other population dynamics. We consider continuous-time level dependent quasi-birth-and-death processes (LDQBDs) extended by catastrophes, which means that the transition rates are allowed to depend on the process level and additionally in each state the level component may drop to zero such that the generator matrix deviates from the block tridiagonal form in that the first block column is allowed to be completely occupied. A matrix analytic algorithm (MAA) for computing the stationary distribution of such processes is introduced that extends and generalizes similar algorithms for LDQBDs without catastrophes. The algorithm is applied in order to analyze M/M/c queues in random environment with catastrophes and state dependent rates. We present a detailed steady state analysis by computing the stationary distribution for different parameter sets, thereby focusing on the marginal probabilities of the level component which represents the number of customers. It turns out that the stationary marginal distribution is bimodal in the sense that it has two local modes that significantly depend on the specific parameters and rates. We also study the efficiency of our matrix analytic algorithm (MAA). Comparisons with standard solution algorithms for Markov chains demonstrate its superiority in terms of runtime and memory requirements.