text: We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed proportions. When one of the stations becomes empty, the total service capacity is given to the non-empty station. Moreover, arrival rates depend on the state of the network. The system is described by a Markov modulated random walk in the quarter plane representing the number of jobs in the two stations and the state of the network. By applying the generating function approach, we first apply the power series approximation method to obtain power series expansions of the generating function of the stationary queue lengths for both network states. Then, we also provide a way to derive the generating function of the stationary queue lengths for both network states in terms of the solution of a Riemann-Hilbert boundary value problem. Numerical results are obtained to show insights in the system performance.
  @cite_26: A steady-state M M N queuing system where each server is subject to random breakdowns of exponentially distributed duration is studied and analyzed. The moment generating function of the queue size is obtained in explicit form for N≦ 2. For larger values of N a numerical method is suggested.
  @cite_32: Jobs generated by a single Poisson source can be routed through N alternative gateways, modelled as parallel M M 1 queues. The servers are subject to random breakdowns which leave their corresponding queues intact, but may affect the routing of jobs during the subsequent repair periods. The marginal equilibrium queue size distributions are determined by spectral expansion. This can be done, at least in principle, for any number of queues. Several routing strategies are evaluated and compared empirically. Numerical results, including optimal routine are presented and possible generalizations are considered. >
  @cite_23: In this paper we characterize the queue-length distribution as well as the waiting time distribution of a single-server queue which is subject to service interruptions. Such queues arise naturally in computer and communication problems in which customers belong to different classes and share a common server under some complicated service discipline. In such queues, the viewpoint of a given class of customers is that the server is not available for providing service some of the time, because it is busy serving customers from a different class. A natural special case of these queues is the class of preemptive priority queues. In this paper, we consider arrivals according the Markovian Arrival Process (MAP) and the server is not available for service at certain times. The service times are assumed to have a general distribution. We provide numerical examples to show that our methods are computationally feasible.
  @cite_2: A computer communication network with window flow control is modeled by a closed multichain queueing network. The severe computational limitation of previous solution algorithms is overcome with a heuristic derived from the recently found mean value analysis. A large numerical example is given.
  @cite_34: This paper deals with the approximate analysis and application of an unreliable closed queueing network to model the performance of a flexible manufacturing system. The service stations in the network are subject to breakdown and repair when active. An exact equivalent network is represented with two-stage Coxian service stations. We approximate the equivalent network by assuming exponentiality for the service completion time, which has a two-stage Coxian distribution. We validate the approximation for a wide range of model parameters and demonstrate the robustness of queueing network formulae to the assumption of exponentiality.
  @cite_10: This paper deals with a two-node Jackson's network which is subject to breakdowns. The system is analyzed in steady state. Generating functions are obtained by solving a functional equation in two variables with the aid of the theory of boundary value problems for regular functions. The numerical implementation of the method is discussed.
  @cite_12: This paper deals with two parallel processors interacting only during breakdown. The system is analyzed in the case where the load is not lost, and in steady state. Generating functions are obtained by solving a functional equation in two complex variables with the aid of the theory of boundary value problems for regular functions.
  @cite_17: 
summary: Most of the existing studies involving breakdowns have concentrated on models with a single job queue served by one or more processors, e.g. @cite_23 @cite_26 . Other related results where jobs from a single source are directed to one of several parallel queues, and where breakdowns result in the loss of jobs, or the direct transfer to other queues are given in @cite_17 @cite_12 @cite_32 . A network of two nodes subject to breakdowns and repairs was also analysed in @cite_10 . Approximate solutions to obtain performance measures, based on replacing an interruptable server with an uninterruptable but slower one, choosing the new service rate without affecting the overall service capacity was given in @cite_2 @cite_34 .