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Markovmodulated infiniteserver queues:
"... This paper studies an infiniteserver queue in a semiMarkov environment: the queue’s input rate is modulated by a semiMarkovian background process, and the service times are assumed to be exponentially distributed. The primary objective of this paper is to propose approximations for the queueleng ..."
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This paper studies an infiniteserver queue in a semiMarkov environment: the queue’s input rate is modulated by a semiMarkovian background process, and the service times are assumed to be exponentially distributed. The primary objective of this paper is to propose approximations for the queue
TIMESCALING LIMITS FOR MARKOVMODULATED INFINITESERVER QUEUES
"... ABSTRACT. In this paper we study semiMarkov modulated M/M/ ∞ queues, which are to be understood as infiniteserver systems in which the Poisson input rate is modulated by a Markovian background process (where the times spent in each of its states are assumed deterministic), and the service times ar ..."
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Cited by 6 (4 self)
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ABSTRACT. In this paper we study semiMarkov modulated M/M/ ∞ queues, which are to be understood as infiniteserver systems in which the Poisson input rate is modulated by a Markovian background process (where the times spent in each of its states are assumed deterministic), and the service times
MARKOVMODULATED INFINITESERVER QUEUES WITH GENERAL SERVICE TIMES
"... ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with an arrival rate that equals λi when an external Markov process is in state i. The service times have a general distribution that depends on the state of the background process upon ar ..."
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Cited by 2 (0 self)
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ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with an arrival rate that equals λi when an external Markov process is in state i. The service times have a general distribution that depends on the state of the background process upon
A FUNCTIONAL CENTRAL LIMIT THEOREM FOR A MARKOVMODULATED INFINITESERVER QUEUE
"... ABSTRACT. The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markovmodulated arrival rate and an exponential decay rate. We analyze the distributional properties of M, the number of molecules, under specific timescaling; the background process is sp ..."
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is sped up by Nα, the arrival rates are scaled by N, for N large. A functional central limit theorem is derived for M, which after centering and scaling, converges to an OrnsteinUhlenbeck process. A dichotomy depending on α is observed. For α ≤ 1 the parameters of the limiting process contain
A FUNCTIONAL CENTRAL LIMIT THEOREM FOR A MARKOVMODULATED INFINITESERVER QUEUE
"... ABSTRACT. The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markovmodulated arrival rate and an exponential decay rate. We analyze the distributional properties of M, the number of molecules, under specific timescaling; the background process is spe ..."
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is sped up by N α, the arrival rates are scaled by N, for N large. A functional central limit theorem is derived for M, which after centering and scaling, converges to an OrnsteinUhlenbeck process. A dichotomy depending on α is observed. For α ≤ 1 the parameters of the limiting process contain
RARE EVENT ANALYSIS OF MARKOVMODULATED INFINITESERVER QUEUES: A POISSON LIMIT
"... ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factorN and the rates νij of the background process byN1+ε ..."
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ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factorN and the rates νij of the background process byN1
A LARGEDEVIATIONS ANALYSIS OF MARKOVMODULATED INFINITESERVER QUEUES
"... ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factor N, tail probabilities are examined when letting N te ..."
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ABSTRACT. This paper studies an infiniteserver queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factor N, tail probabilities are examined when letting N
Analysis of an InfiniteServer Queue with
 Batch Markovian Arrival Streams”, Queueing Systems
, 2002
"... Abstract. This paper considers an infiniteserver queue with multiple batch Markovian arrival streams. The service time distribution of customers may be different for different arrival streams, and simultaneous batch arrivals from more than one stream are allowed. For this queue, we first derive a s ..."
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Cited by 1 (0 self)
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numerical examples are provided to discuss the impact of system parameters on the performance. Keywords: Infiniteserver queue, Markovian arrival stream, batch arrivals, timedependent analysis, limiting distribution
A Markovmodulated characterization of packetized voice and data traffic and related statistical multiplexer performance
 IEEE J. ON SELECTED AREAS IN COMMUN
, 1986
"... We study the performance of a statistical multiplexer whose inputs consist of a superposition of packetized voice sources and data. The performance analysis predicts voice packet delay distributions, which usually have a stringent requirement, as well as data packet delay distributions. The superpos ..."
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Cited by 285 (4 self)
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. The superposition is approximated by a correlated Markov modulated Poisson process (MMPP), which is chosen such that several of its statistical characteristics identically match those of the superposition. Matrix analytic methods are then used to evaluate system performance measures. In particular, we obtain
Results 1  10
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