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## On queues with Markov-modulated service rates. Queueing Systems (2005)

Venue: | Queueing Systems |

Citations: | 6 - 0 self |

### Citations

858 |
Matrix-Geometric Solutions in Stochastic Models
- Neuts
- 1981
(Show Context)
Citation Context ...A0 + RA1 + R 2 A2 = 0. (8) Equation (8) has to be used recursively to solve for R. There is a lot of research going on to find R efficiently but we will not go into those details in this paper. Neuts =-=[19]-=- defines infinitestate Markov chains with a repetitive structure with state space partitioned into the boundary states } ∀i ≥ 1, that correspond to the repetitive S (0) = {s1 0 , ....., sn0 } and a se... |

317 | Effective bandwidth of general markovian traffic sources and admission control of high speed networks
- Elwalid, Mitra
- 1993
(Show Context)
Citation Context ...tle’s law, λW ). The next question is whether it would be possible to obtain the distribution of any of the performance measures. As it turns out, in the 1990’s several researchers (Elwalid and Mitra =-=[10]-=-, Kelly [13], Kesidis et al [14], Courcoubetis and Weber [8]) used the method of large deviations to obtain tail distributions of the system workload. In that spirit, 16sA (t) W (t) C Figure 3: Single... |

311 |
Multiservice Loss Models for Broadband Telecommunication Networks
- Ross
- 1995
(Show Context)
Citation Context ...In the communication networks community, researchers have considered both these classes separately for analysis. Research focusing on streaming traffic can be categorized as ‘loss networks’ (see Ross =-=[24]-=-, Roberts [23], Kaufman [12]) while research that caters to the needs of elastic traffic can be categorized as ‘delay networks’. Bonald and Proutiere [4] considered a queueing network with varying flo... |

277 |
Modeling and Analysis of Stochastic Systems
- Kulkarni
- 1995
(Show Context)
Citation Context ...j) = 1, (1) j�=i ) is obtained by solving the set of equations f 2 i 2 E(Ti ) − fi � qijE(T j�=i 2 � j ) = 2(1 + qijE(Tj)), (2) j�=i Proof. The proof applies first step analysis (Dorman [9], Kulkarni =-=[15]-=-) based on the Laplace Stieltjes transform (LST) of the conditional service time. Let Ti be the random variable denoting total service time that begins in state i for an arbitrary customer in steady s... |

232 | Effective bandwidths for multiclass Markov fluids and other ATM sources
- Kesidis, Walrand, et al.
- 1993
(Show Context)
Citation Context ...on is whether it would be possible to obtain the distribution of any of the performance measures. As it turns out, in the 1990’s several researchers (Elwalid and Mitra [10], Kelly [13], Kesidis et al =-=[14]-=-, Courcoubetis and Weber [8]) used the method of large deviations to obtain tail distributions of the system workload. In that spirit, 16sA (t) W (t) C Figure 3: Single Buffer Model we will take advan... |

219 |
Blocking in a shared resource environment
- Kaufman
- 1981
(Show Context)
Citation Context ...s community, researchers have considered both these classes separately for analysis. Research focusing on streaming traffic can be categorized as ‘loss networks’ (see Ross [24], Roberts [23], Kaufman =-=[12]-=-) while research that caters to the needs of elastic traffic can be categorized as ‘delay networks’. Bonald and Proutiere [4] considered a queueing network with varying flow-rate (elastic traffic as t... |

168 |
Note on effective bandwidth,” in Stochastic Networks: Theory and Applications. ser. Royal Statistical Society Lecture Notes
- Kelly
- 1996
(Show Context)
Citation Context ...W ). The next question is whether it would be possible to obtain the distribution of any of the performance measures. As it turns out, in the 1990’s several researchers (Elwalid and Mitra [10], Kelly =-=[13]-=-, Kesidis et al [14], Courcoubetis and Weber [8]) used the method of large deviations to obtain tail distributions of the system workload. In that spirit, 16sA (t) W (t) C Figure 3: Single Buffer Mode... |

86 |
A service system with heterogeneous user requirements, volume Performance
- Roberts
- 1981
(Show Context)
Citation Context ...cation networks community, researchers have considered both these classes separately for analysis. Research focusing on streaming traffic can be categorized as ‘loss networks’ (see Ross [24], Roberts =-=[23]-=-, Kaufman [12]) while research that caters to the needs of elastic traffic can be categorized as ‘delay networks’. Bonald and Proutiere [4] considered a queueing network with varying flow-rate (elasti... |

69 | Insensitive bandwidth sharing in data networks
- Bonald, Proutière
(Show Context)
Citation Context ...n be categorized as ‘loss networks’ (see Ross [24], Roberts [23], Kaufman [12]) while research that caters to the needs of elastic traffic can be categorized as ‘delay networks’. Bonald and Proutiere =-=[4]-=- considered a queueing network with varying flow-rate (elastic traffic as the primary flow) and studied flow-level dynamics. However, very few articles (such as Quieja [20]) have considered both traff... |

36 | Effective bandwidth for stationary sources,” Probability in Engineering and
- Courcoubetis, Weber
- 1995
(Show Context)
Citation Context ...sible to obtain the distribution of any of the performance measures. As it turns out, in the 1990’s several researchers (Elwalid and Mitra [10], Kelly [13], Kesidis et al [14], Courcoubetis and Weber =-=[8]-=-) used the method of large deviations to obtain tail distributions of the system workload. In that spirit, 16sA (t) W (t) C Figure 3: Single Buffer Model we will take advantage of the theory of large ... |

14 | The analysis of queues with time-varying rates for telecommunication models
- Massey
(Show Context)
Citation Context ..., Boxma & Kurkova [5], and BaykalGursoy & Xiao [3]). However, there are several articles on service rate control where service rate is time-varying (for example, Sharma [25]). Some papers like Massey =-=[18]-=- talk about queues with deterministic time varying rates in telecommunication models. Also, Collings and Stoneman [7] considers a M/M/∞ queue with deterministic time varying arrivals and service rates... |

13 |
Bounds for fluid models driven by semi-markov inputs
- Gautam, Kulkarni, et al.
- 1999
(Show Context)
Citation Context ...brings need not be exponential, we can still obtain the effective bandwidth. In fact the {Z(t), t ≥ 0} process need not even be a CTMC. If the input process is a semi-Markov process (See Gautam et al =-=[11]-=-) or a Markov regenerative process (See Kulkarni [16]), computing effective bandwidth is possible. Therefore these tail probabilities can be applied to a much more general setting than what is conside... |

12 |
Effective bandwidths for Markov regenerative sources
- Kulkarni
- 1996
(Show Context)
Citation Context ...he effective bandwidth. In fact the {Z(t), t ≥ 0} process need not even be a CTMC. If the input process is a semi-Markov process (See Gautam et al [11]) or a Markov regenerative process (See Kulkarni =-=[16]-=-), computing effective bandwidth is possible. Therefore these tail probabilities can be applied to a much more general setting than what is considered here. One of the main applications of tail distri... |

11 |
The M/G/1 queue with two service speeds
- Boxma, Kurkova
- 2001
(Show Context)
Citation Context ...es service. So, unlike in our paper, the server speed cannot change during the middle of a service. In addition, the service rates mainly take only two values in Zhou and Gans [28]. Boxma and Kurkova =-=[5]-=- considers an M/G/1 queue where the speed of the server alternates between two values with high speed periods having exponential distribution and low speed periods having a general distribution. Motiv... |

9 | On queues with inter-arrival times proportional to service times
- Cidon, Guerin, et al.
- 1991
(Show Context)
Citation Context ...al times. There are many articles (for e.g. Takahashi and Wang [26], Ahn and Jeon [2]) that analyze queues with Markov modulated arrivals. Some researchers like Adan and Kulkarni [1], and Cidon et al =-=[6]-=-, analyze queues that have inter-arrival times and service times dependent on each other. On the whole, researchers have focussed more on analyzing queues with time varying and Markov modulated arriva... |

5 |
Stochastic Decomposition in M/M/∞ queues with Markov Modulated Service Rates” Queueing Systems
- Baykal-Gursoy, Xiao
- 2004
(Show Context)
Citation Context ...ion. Motivated by the transportation system where if an incident occurs on a road segment all the vehicles on the road have to lower their speed until that incident is cleared, Baykal-Gursoy and Xiao =-=[3]-=- considers an M/M/∞ queueing system subject to random interruptions of exponential distributed durations. Another related article is Núñez-Queija [20] where the author considers a special case of what... |

4 |
Single server queue with Markov dependent inter-arrival and service times
- Adan, Kulkarni
(Show Context)
Citation Context ...th time varying arrival times. There are many articles (for e.g. Takahashi and Wang [26], Ahn and Jeon [2]) that analyze queues with Markov modulated arrivals. Some researchers like Adan and Kulkarni =-=[1]-=-, and Cidon et al [6], analyze queues that have inter-arrival times and service times dependent on each other. On the whole, researchers have focussed more on analyzing queues with time varying and Ma... |

3 |
The M/M/ queue with varying arrival and service rates
- Collings, Stoneman
- 1976
(Show Context)
Citation Context ... service rate is time-varying (for example, Sharma [25]). Some papers like Massey [18] talk about queues with deterministic time varying rates in telecommunication models. Also, Collings and Stoneman =-=[7]-=- considers a M/M/∞ queue with deterministic time varying arrivals and service rates. But, the Markov Modulated service rate problem in which the service rates vary according to an environment process ... |

3 | Algorithmic analysis of stochastic models - the changing face of mathematics - Ramaswami - 2000 |

2 |
Invariant measures for quasi-birth and death processes”, Stochastic Models
- Latouche, Pierce, et al.
- 1997
(Show Context)
Citation Context ...rocess cannot skip adjacent states and hence it is called “skip free” in the states. Birthdeath process is a special case of more general class called Quasi-birth-death process. As per Latouche et al =-=[17]-=-, the definition for quasi birth-death process is as follows. Definition: A continuous time Quasi-Birth-Death (QBD) process is a continuous time Markov process whose infinitesimal generator matrix is ... |

2 |
Queues with service rate controlled by a delayed feedback
- Sharma
- 2001
(Show Context)
Citation Context ... & Gans [28], Núñez-Queija [20], Boxma & Kurkova [5], and BaykalGursoy & Xiao [3]). However, there are several articles on service rate control where service rate is time-varying (for example, Sharma =-=[25]-=-). Some papers like Massey [18] talk about queues with deterministic time varying rates in telecommunication models. Also, Collings and Stoneman [7] considers a M/M/∞ queue with deterministic time var... |

1 |
Large deviation results for queues with Continuous time Markov modulated
- Ahn, Jeon
- 2000
(Show Context)
Citation Context ...h upon some of the related work. There are several articles in literature that consider queues with time varying arrival times. There are many articles (for e.g. Takahashi and Wang [26], Ahn and Jeon =-=[2]-=-) that analyze queues with Markov modulated arrivals. Some researchers like Adan and Kulkarni [1], and Cidon et al [6], analyze queues that have inter-arrival times and service times dependent on each... |

1 |
Steady state analysis of a queue with varying service rate
- Núñez-Queija
- 1997
(Show Context)
Citation Context ...l that incident is cleared, Baykal-Gursoy and Xiao [3] considers an M/M/∞ queueing system subject to random interruptions of exponential distributed durations. Another related article is Núñez-Queija =-=[20]-=- where the author considers a special case of what we consider in this paper, namely the environment process is a specific birth and death process (i.e. queue length process of an M/M/c/c queue). For ... |

1 |
Mamsolver: A matix analytical method tool
- Riska, Smirni
(Show Context)
Citation Context ... is frequently done numerically. For a level independent infinite level CTMC, R is obtained as follows. Computation of matrix R: The matrix R has a following quadratic relation (Ramaswami [21], Riska =-=[22]-=-): A0 + RA1 + R 2 A2 = 0. (8) Equation (8) has to be used recursively to solve for R. There is a lot of research going on to find R efficiently but we will not go into those details in this paper. Neu... |

1 |
Approximate analysis of a queueing system with Markov modulated arrivals
- Takahashi, Wang
- 1990
(Show Context)
Citation Context ... organized, we touch upon some of the related work. There are several articles in literature that consider queues with time varying arrival times. There are many articles (for e.g. Takahashi and Wang =-=[26]-=-, Ahn and Jeon [2]) that analyze queues with Markov modulated arrivals. Some researchers like Adan and Kulkarni [1], and Cidon et al [6], analyze queues that have inter-arrival times and service times... |

1 |
Modeling Complex Queuing Situations with
- Thorne
(Show Context)
Citation Context ...f explanation would ensure smoother reading. 4.1 Quasi-birth and death process In order to understand Quasi-birth-death process, we will start with the definition of birth-death process as per Thorne =-=[27]-=-. Definition: The continuous-time Markov process {Y (t) : t ≥ 0} is a birth-death process if the only two possible transitions are n → n + 1 with birth rates q(n, n + 1), n ≥ 0, and n → n − 1 with dea... |

1 | A single-server queue with Markov modulated service times
- Zhou, Gans
- 1999
(Show Context)
Citation Context ...to open a new avenue of research problems, as the stochastically varying server speed problem has received very little attention. There are a few articles that are related. The first is Zhou and Gans =-=[28]-=-, where the authors state that time-varying service rate problems have not been studied in the literature. The key difference between Zhou and Gans [28] and ours is that, they consider service speeds ... |