Queueing systems with service interruptions
Operations Research
A queue with service interruptions in an alternating random environment
Operations Research
A single server queue with service interruptions
Queueing Systems: Theory and Applications
Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates
Queueing Systems: Theory and Applications
M/M/C queues with Markov modulated service processes
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Queues with system disasters and impatient customers when system is down
Queueing Systems: Theory and Applications
The M/M/∞ queue in a random environment
Queueing Systems: Theory and Applications
M/M/∞ queues in semi-Markovian random environment
Queueing Systems: Theory and Applications
Heavy-traffic limits for many-server queues with service interruptions
Queueing Systems: Theory and Applications
On a queuing model with service interruptions
Probability in the Engineering and Informational Sciences
Service Interruptions in Large-Scale Service Systems
Management Science
Maintenance of deteriorating single server queues with random shocks
Computers and Industrial Engineering
Optimal maintenance policies for systems subject to a Markovian operating environment
Computers and Industrial Engineering
Stochastic decomposition of the M/G/∞ queue in a random environment
Operations Research Letters
Computers and Industrial Engineering
Computers and Industrial Engineering
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Motivated by the need to study traffic incident management, we consider a Markovian infinite server queue that is subjected to randomly occurring shocks. These shocks affect the service of all servers to deteriorate, i.e., increase the service time of all servers, and might also cause other shocks, thus causing further service deterioration. There are a finite number of service levels, zero corresponding to the normal service with the highest service rate and the last level corresponding to the slowest service rate which could even be equal to zero, implying the complete service breakdown. The repair process is performed only at the last level. These types of queues also represent an approximation of multi-server call-centers with deteriorating service. We derive the mean and variance of the stationary number in the system, and show that the mean is convex with respect to the repair rate. Furthermore, we study the optimal repair rate that minimizes the expected long-run average cost incurred due to delay and repairs. We show that the expected total cost per unit time as a function of repair rate is unimodal. We derive conditions under which the cost function is in one of three simple forms, so that the optimum repair rate can easily be obtained. Numerical examples are also provided.