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## Scheduling in a Queueing System with Asynchronously Varying Service Rates

Venue: | Probability in the Engineering and Informational Sciences |

Citations: | 94 - 8 self |

### Citations

3075 |
An Introduction to Probability Theory and Its Applications
- Feller
- 1971
(Show Context)
Citation Context ...nt at t, whichever is less). We assume that, within each type, customers are served in the order of their arrival in the system. The random server state process m is assumed to be an irreducible (see =-=[12]-=-) discrete time Markov chain with the (nite) state space M . The (unique) stationary distribution of this Markov chain we denote by = ( 1 ; : : : ; M ). Note that, due to irreducibility, m > 0... |

947 | Stability Properties of Constrained Queueing Systems and Scheduling Policies for Maximal Throughput in Multihop Radio Networks,”
- Tassiulas, Ephremides
- 1992
(Show Context)
Citation Context ...s of results on the stability of MaxWeight type scheduling algorithms in queueing networks and in input-buered crossbar 2 switches. Thesrst results of this type were obtained by Tassiulas-Ephremides =-=[23, 24]-=- in the context of wireless systems. For the switch scheduling stability results, see papers [15, 17, 10], and a recent paper [10]. In the context of interactive parallel server systems and systems wi... |

806 | Opportunistic beamforming using dumb antennas
- Viswanath, Tse, et al.
- 2002
(Show Context)
Citation Context ...hich do not take channel conditions into account. A scheduling rule providing proportional fairness in the achieved long-term throughput of dierent users was proposed and analyzed in [25]. (See also =-=[27]-=-.) The QoS of a data user can be dened in dierent ways. If data users are real-time users, then the packet delays of eachsow need to be kept below a certain threshold. This means that the primary go... |

526 | Achieving 100% Throughput in an InputQueued Switch
- Mekkittikul, McKeown
- 1999
(Show Context)
Citation Context ...ut-buered crossbar 2 switches. Thesrst results of this type were obtained by Tassiulas-Ephremides [23, 24] in the context of wireless systems. For the switch scheduling stability results, see papers =-=[15, 17, 10]-=-, and a recent paper [10]. In the context of interactive parallel server systems and systems with randomly varying connectivity, MaxWeight-type stability results were obtained in [3, 5]. (See also [4]... |

276 | Dynamic server allocation to parallel queues with randomly varying connectivity
- Tassiulas, Ephremides
- 1993
(Show Context)
Citation Context ...s of results on the stability of MaxWeight type scheduling algorithms in queueing networks and in input-buered crossbar 2 switches. Thesrst results of this type were obtained by Tassiulas-Ephremides =-=[23, 24]-=- in the context of wireless systems. For the switch scheduling stability results, see papers [15, 17, 10], and a recent paper [10]. In the context of interactive parallel server systems and systems wi... |

222 | The Throughput of Data Switches with and without Speedup
- Dai, Prabhakar
- 2000
(Show Context)
Citation Context ...ut-buered crossbar 2 switches. Thesrst results of this type were obtained by Tassiulas-Ephremides [23, 24] in the context of wireless systems. For the switch scheduling stability results, see papers =-=[15, 17, 10]-=-, and a recent paper [10]. In the context of interactive parallel server systems and systems with randomly varying connectivity, MaxWeight-type stability results were obtained in [3, 5]. (See also [4]... |

165 | Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. The Annals of Applied Probability,
- Stolyar
- 2004
(Show Context)
Citation Context ... proportional to each other, and thus a MaxWeight-type algorithm using Q j (t), W j (t) or a linear combination V j (t) are in some sense \indistinguishable" in thesuid limit. It is shown recently in =-=[21]-=-, which analyzes a more general (described in Section 4.2) version of our model, that, in addition to throughput optimality, MaxWeight-type rules have certain asymptotic optimality properties when the... |

140 |
Ergodicity of stochastic processes describing the operation of open queueing networks.
- Rybko, Stolyar
- 1992
(Show Context)
Citation Context ...y, ifsow j has a high arrival rate and we want to bound its buer space requirements then (Q) j should be large relative to (W ) j . To prove our stability results, we use thesuid limit technique =-=[19, 8, 7, 20, 9]-=-. (For a MaxWeight-type rule, the technique was also used in [10] in a \switch" model context.) Use of this technique makes the above described generalization very natural. Roughly speaking, in the \ ... |

87 | Fluid approximations and stability of multiclass queueing networks: workconserving disciplines
- Chen
- 1995
(Show Context)
Citation Context ...y, ifsow j has a high arrival rate and we want to bound its buer space requirements then (Q) j should be large relative to (W ) j . To prove our stability results, we use thesuid limit technique =-=[19, 8, 7, 20, 9]-=-. (For a MaxWeight-type rule, the technique was also used in [10] in a \switch" model context.) Use of this technique makes the above described generalization very natural. Roughly speaking, in the \ ... |

74 | CDMA data QoS scheduling on the forward link with variable channel conditions
- Andrews, Kumaran, et al.
- 2000
(Show Context)
Citation Context ..., MaxWeight-type rules have certain asymptotic optimality properties when the system is heavily loaded. Practical implications of using M-LWDF to provide QoS for real time data users are addressed in =-=[2]-=-. In particular, we show in [2] that the M-LWDF discipline, with \appropriately" chosen parameterssi , provides good QoS dened in terms of the probabilities of packet delays exceeding predened thres... |

71 | Largest weighted delay first scheduling: large deviations and optimality.
- Stolyar, Ramanan
- 2001
(Show Context)
Citation Context ... forsow j, j (t) is the server capacity forsow j at time t, andsand thesj 's are arbitrary positive constants. (The name M-LWDF is because this discipline is a generalization of the LWDF discipline =-=[1, 22]-=-.) Moreover, as we discuss in Section 4, our result actually holds for a quite wide class of disciplines (of which M-LWDF is a member), and a more general class of models. In particular, the throughpu... |

69 |
On stability of multiclass queueing networks: a relaxed sufficient condition via fluid processes.
- Stolyar
- 1995
(Show Context)
Citation Context ...y, ifsow j has a high arrival rate and we want to bound its buer space requirements then (Q) j should be large relative to (W ) j . To prove our stability results, we use thesuid limit technique =-=[19, 8, 7, 20, 9]-=-. (For a MaxWeight-type rule, the technique was also used in [10] in a \switch" model context.) Use of this technique makes the above described generalization very natural. Roughly speaking, in the \ ... |

42 |
Ergodicity, continuity, and analyticity of countable markov chains
- Malyshev, Menshikov
- 1979
(Show Context)
Citation Context ...) will be supplied with the upper index (n). The following theorem follows from the state depenent Lyapunov-type stability criteria for countable Markov chains, obtainedsrst by Malyshev and Menshikov =-=[16]-=-. Theorem 4 Suppose there exist > 0 and an integer T > 0 such that for any sequence of processes fS (n) ; n = 1; 2; : : :g, we have lim sup n!1 E[ 1 n kS (n) (nT )k] 1 : (10) Then S is stable. ... |

38 |
Numerical Methods for Constrained Optimization
- Gill, Murray, et al.
- 1974
(Show Context)
Citation Context ...M; i = 1; : : : ; N: (7) From the denition of v we know that = 1 and = solve this linear program, with constraints (6) satised as equalities. Then, by Kuhn-Tucker theorem (see for example =-=[13]-=-), there exists a set of non-negative Lagrange multipliers 0 ; 1 ; : : : ; N such that = 1 and = also solve the following linear program (with the same value of the maximum): max ;f mi... |

29 |
Queueing networks with interacting service resources
- Armony, Bambos
- 1999
(Show Context)
Citation Context ...e papers [15, 17, 10], and a recent paper [10]. In the context of interactive parallel server systems and systems with randomly varying connectivity, MaxWeight-type stability results were obtained in =-=[3, 5]-=-. (See also [4], which is a recent extension of [3].) The underlying intuition behind the stability of a MaxWeight-type algorithm is the fact that it minimizes the drift of a Lyapunov function of the ... |

19 |
Forward link multiuser diversity through rate adaptation and scheduling
- Tse
(Show Context)
Citation Context ...duling schemes which do not take channel conditions into account. A scheduling rule providing proportional fairness in the achieved long-term throughput of dierent users was proposed and analyzed in =-=[25]-=-. (See also [27].) The QoS of a data user can be dened in dierent ways. If data users are real-time users, then the packet delays of eachsow need to be kept below a certain threshold. This means tha... |

16 |
A Starvation Free Algorithm for Achieving 100% Throughput
- Mckeown, Mekkittikul
- 1996
(Show Context)
Citation Context ...ut-buered crossbar 2 switches. Thesrst results of this type were obtained by Tassiulas-Ephremides [23, 24] in the context of wireless systems. For the switch scheduling stability results, see papers =-=[15, 17, 10]-=-, and a recent paper [10]. In the context of interactive parallel server systems and systems with randomly varying connectivity, MaxWeight-type stability results were obtained in [3, 5]. (See also [4]... |

13 |
On the positive Harris recurrence for open multiclass queueing networks: a unified approach via fluid limit models
- Dai
- 1995
(Show Context)
Citation Context |

8 |
On parallel queueing with random server connectivity and routing constraints
- Bambos, Michailidis
- 2002
(Show Context)
Citation Context ...e papers [15, 17, 10], and a recent paper [10]. In the context of interactive parallel server systems and systems with randomly varying connectivity, MaxWeight-type stability results were obtained in =-=[3, 5]-=-. (See also [4], which is a recent extension of [3].) The underlying intuition behind the stability of a MaxWeight-type algorithm is the fact that it minimizes the drift of a Lyapunov function of the ... |

8 |
Stability and convergence of moments for open multiclass queueing networks via fluid limit models
- Dai, Meyn
- 1995
(Show Context)
Citation Context |

6 |
Data Rate Scheduling Algorithms and Capacity Estimates for the CDMA Forward Link
- Andrews, Kumaran, et al.
- 1999
(Show Context)
Citation Context ... forsow j, j (t) is the server capacity forsow j at time t, andsand thesj 's are arbitrary positive constants. (The name M-LWDF is because this discipline is a generalization of the LWDF discipline =-=[1, 22]-=-.) Moreover, as we discuss in Section 4, our result actually holds for a quite wide class of disciplines (of which M-LWDF is a member), and a more general class of models. In particular, the throughpu... |

6 |
Principles of Spread Spectrum Communication
- CDMA
- 1995
(Show Context)
Citation Context ...@research.bell-labs.com z University of Michigan, Ann Arbor, MI, rvijayak@engin.umich.edu 1 The variable channel problem arises, for example, in the 3G CDMA High Data Rate (HDR) system [6]. (See also =-=[26]-=- for a background on CDMA wireless systems.) In HDR, multiple mobile users in a cell share the same CDMA wireless channel. On the downlink (the link from cell base station to users), time is divided i... |

3 |
CDMA/HDR: A Bandwidth EÆcient High Speed Wireless Data Service for Nomadic Users
- Bender, Grob, et al.
- 2000
(Show Context)
Citation Context ...olyar,pwhitingg@research.bell-labs.com z University of Michigan, Ann Arbor, MI, rvijayak@engin.umich.edu 1 The variable channel problem arises, for example, in the 3G CDMA High Data Rate (HDR) system =-=[6]-=-. (See also [26] for a background on CDMA wireless systems.) In HDR, multiple mobile users in a cell share the same CDMA wireless channel. On the downlink (the link from cell base station to users), t... |