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## Order optimal delay for opportunistic scheduling in multi-user wireless uplinks and downlinks (2006)

Venue: | Proc. of Allerton Conf. on Communication, Control, and Computing (invited paper |

Citations: | 43 - 6 self |

### Citations

2192 | Data Networks
- Bertsekas, Gallager
- 1992
(Show Context)
Citation Context ...yields E {µ1(t) + . . . µN (t)} = rN, so that E {µi(t)} = rN /N for all i ∈ {1, . . . , N}. B. The Single-Queue Lower Bound A simple lower bound on the average backlog (and hence, by Little’s Theorem =-=[30]-=-, average delay), can be obtained by using the multiplexing inequality [31]. Specifically, the multiplexing ∑ inequality states that the total queue backlog N i=1 Qi(t) in a system of N queues describ... |

926 | Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks,” Automatic Control
- Tassiulas, Ephremides
- 1936
(Show Context)
Citation Context ...aring problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for satellite, wireless, and ad-hoc mobile systems in [1][2][3][6][7]=-=[12]-=-[13]. The work in [6] develops delay optimality results in the limit as the system loading ρ approaches 1, but does not provide asymptotic results in the number of users. Indeed, the analysis in [6] u... |

926 |
Stochastic Process
- Ross
- 1996
(Show Context)
Citation Context ...t. APPENDIX B — STOCHASTIC INEQUALITIES Here we derive the stochastic comparison result stated in Section IV-A. We first review basic stochastic inequality facts for any random variables X and Y (see =-=[36]-=-). Definition 2: A random variable X is said to be stochastically less than a random variable Y (written X ≤ Y ) if: st. P r[X > ω] ≤ P r[Y > ω] for all real values ω Lemma 4: (Stochastic Coupling [36... |

519 | Achieving 100% throughput in an input-queued switch
- McKeown, Mekkittikul, et al.
- 1999
(Show Context)
Citation Context ...he previous O(N/(1 − ρ)) bound in [7], it has a slightly worse asymptotic in ρ. Much work in the area of dynamic scheduling is developed for computer networks and switching systems, including work in =-=[23]-=-[24][25][26] that uses Lyapunov stability theory. The work in [24] considers max-weight-match (MWM) scheduling in an N ×N packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows th... |

349 | Dynamic power allocation and routing for time varying wireless networks
- Neely, Modiano, et al.
- 2005
(Show Context)
Citation Context ...g problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for satellite, wireless, and ad-hoc mobile systems in [1][2][3][6][7][12]=-=[13]-=-. The work in [6] develops delay optimality results in the limit as the system loading ρ approaches 1, but does not provide asymptotic results in the number of users. Indeed, the analysis in [6] uses ... |

275 | Dynamic server allocation to parallel queues with randomly varying connectivity
- Tassiulas, Ephremides
- 1993
(Show Context)
Citation Context ...tem model is central to the study of channelaware (or “opportunistic”) scheduling in wireless systems, and the model along with many generalizations have been extensively considered in the literature =-=[1]-=--[22]. Landmark work by Tassiulas and Ephremides in [1] characterizes the capacity region of this model, consisting of the set of all arrival rate vectors the system can be configured to stably suppor... |

267 | Resource allocation and cross-layer control in wireless networks
- Georgiadis, Neely, et al.
- 2006
(Show Context)
Citation Context ...on can be given in terms of all possible expected transmission rate vectors that can be achieved by a stationary randomized scheduling policy, as shown below. Lemma 1: (Stationary Randomized Policies =-=[17]-=-[1]) A rate vector λ = (λ1, . . . , λN ) is in the capacity region Λ if and only if there exists a stationary control strategy that chooses a transmission rate vector µ(t) = (µ1(t), . . . , µN (t)) as... |

259 | Fairness and optimal stochastic control for heterogeneous networks - Neely, Modiano, et al. - 2005 |

248 |
Providing quality of service over a shared wireless link
- Andrews, Kumaran, et al.
- 2001
(Show Context)
Citation Context ...and a clearing problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for satellite, wireless, and ad-hoc mobile systems in [1][2]=-=[3]-=-[6][7][12][13]. The work in [6] develops delay optimality results in the limit as the system loading ρ approaches 1, but does not provide asymptotic results in the number of users. Indeed, the analysi... |

219 | The throughput of data switches with and without speedup
- Dai, Prabhakar
- 2000
(Show Context)
Citation Context ...N packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that average delay is no more than cN/(1 − ρ). Various methods of queue groupings are used with Lyapunov functions in [28]=-=[29]-=-[30][31] to achieve low complexity scheduling. While [28][29][30][31] does not primarily focus on delay, it is interesting to note that if an N ×N switch is half loaded (ρ < 1/2) with independent Bern... |

200 | Maximizing queueing network utility subject to stability: Greedy primal-dual algorithm,” Queue - Stolyar - 2005 |

194 | Fair resource allocation in wireless networks using queue-length based scheduling and congestion control - Eryilmaz, Srikant |

185 | Capacity and optimal resource allocation for fading broadcast channels-Part I: Ergodic capacity
- Li, Goldsmith
- 2001
(Show Context)
Citation Context ...derive a similar result for large classes of asymmetric systems, i.e., systems with heterogeneous traffic rates and channel probabilities. Previous work in the area of wireless scheduling is found in =-=[5]-=-[8][9] for systems with an infinite backlog of data, and a clearing problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for sat... |

179 | Energy optimal control for time varying wireless networks
- Neely
- 2006
(Show Context)
Citation Context ..., and E {˜µsum,k(t)} ≤ 1 for all t, the process B(t) satisfies E {B(t)} ≤ B for all t (where B is a finite constant). It follows that the queueing network is strongly stable and hence E {Qi(t)/t} → 0 =-=[18]-=-. Thus: It follows that: lim sup t→∞ 1 t t−1 1 lim t→∞ t τ=0 ∑t−1 τ=0 1 2 ∑ E {˜µsum,k(τ)} = λsum,k E {B(τ)} = [ λtot + ∑ k E { A 2 sum,k which completes the proof of Theorem 2. } − 2 ∑ k λ2 ] sum,kI... |

160 | Optimal opportunistic scheduling in wireless networks - Liu, Chong, et al. - 2003 |

130 | S.P.; “Stability of Queueing Networks and Scheduling Policies
- Kumar, Meyn
- 1995
(Show Context)
Citation Context ...ous O(N/(1 − ρ)) bound in [7], it has a slightly worse asymptotic in ρ. Much work in the area of dynamic scheduling is developed for computer networks and switching systems, including work in [23][24]=-=[25]-=-[26] that uses Lyapunov stability theory. The work in [24] considers max-weight-match (MWM) scheduling in an N ×N packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that avera... |

126 | A practical scheduling algorithm for achieving 100% throughput in input-queued switches
- Mekkittikul, McKeown
(Show Context)
Citation Context ...O(N/(1 − ρ)) bound in [7], it has a slightly worse asymptotic in ρ. Much work in the area of dynamic scheduling is developed for computer networks and switching systems, including work in [23][24][25]=-=[26]-=- that uses Lyapunov stability theory. The work in [24] considers max-weight-match (MWM) scheduling in an N ×N packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that average d... |

95 | Power Allocation and Routing in Multibeam Satellites with Time-varying Channels
- Neely, Modiano, et al.
- 2003
(Show Context)
Citation Context ...s use the stochastic coupling technique of [1], which seems to require this symmetry. Further, the actual average delay achieved by these strategies is unknown, even in these symmetric cases. Work in =-=[7]-=- computes upper bounds on the delay of stabilizing largestqueue type strategies. However, these bounds grow linearly in the number of users N. Specifically, the delay bound is given by O(N/(1−ρ)), whe... |

63 | Optimal energy and delay tradeoffs for multi-user wireless downlinks - Neely - 2007 |

60 | Pathwise Optimality of the Exponential Scheduling Rule for Wireless Channels
- Shakkottai, Srikant, et al.
- 2001
(Show Context)
Citation Context ... a clearing problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for satellite, wireless, and ad-hoc mobile systems in [1][2][3]=-=[6]-=-[7][12][13]. The work in [6] develops delay optimality results in the limit as the system loading ρ approaches 1, but does not provide asymptotic results in the number of users. Indeed, the analysis i... |

52 |
Applied Probability and Queues, Second Edition
- Asmussen
- 2003
(Show Context)
Citation Context ...e ties randomly and uniformly over all groups. This tie breaking rule also ensures the vector queueing process Q(t) evolves according to a discrete time Markov chain, in which case Foster’s criterion =-=[32]-=- can be used to ensure the chain has a valid steady state with steady state queue occupancies Qi. If inputs are independent and Bernoulli or Poisson, then the expression (9) can be simplified to ∑ i Q... |

46 |
Bounds on the capacity region of multihop wireless networks under distributed greedy scheduling
- Wu, Srikant
- 2006
(Show Context)
Citation Context ...et switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that average delay is no more than O(N/(1 − ρ)). Various methods of queue groupings are used with Lyapunov functions in [26][27]=-=[28]-=- to achieve low complexity scheduling. While [26][27][28] does not primarily focus on delay, it is interesting to note that if an N × N switch is half loaded (ρ < 1/2) with independent Bernoulli or Po... |

42 |
Throughput and delay optimal resource allocation in multiaccess fading channels
- Yeh, Cohen
(Show Context)
Citation Context ...Foundation grant OCE 0520324, the DARPA IT-MANET program. and identical channel probabilities for each link, the LCQ policy minimizes average delay. This delay optimality result is generalized in [4] =-=[10]-=-, where a delay optimal policy is developed for selecting transmission rates within the polytope capacity region associated with the Gaussian multiple access channel, and in [14] where generalizations... |

40 | Dynamic global packet routing in wireless networks - Kahale, Wright - 1997 |

37 | Capacity and optimal power allocation for fading broadcast channels with minimum rates
- Jindal, Goldsmith
- 2003
(Show Context)
Citation Context ... a similar result for large classes of asymmetric systems, i.e., systems with heterogeneous traffic rates and channel probabilities. Previous work in the area of wireless scheduling is found in [5][8]=-=[9]-=- for systems with an infinite backlog of data, and a clearing problem in a system with N links and a fixed amount of data is treated in [11]. Stable scheduling and queueing is considered for satellite... |

34 | Super-fast delay tradeoffs for utility optimal fair scheduling in wireless networks
- Neely
(Show Context)
Citation Context ...model is central to the study of channelaware (or “opportunistic”) scheduling in wireless systems, and the model along with many generalizations have been extensively considered in the literature [1]-=-=[22]-=-. Landmark work by Tassiulas and Ephremides in [1] characterizes the capacity region of this model, consisting of the set of all arrival rate vectors the system can be configured to stably support. Th... |

31 | Tsitsiklis, “Optimal transmission scheduling in symmetric communication models with intermittent connectivity
- Ganti, Modiano, et al.
- 2007
(Show Context)
Citation Context ...ed independently of the number of users N, for any value of ρ < 1. We note that a different approach to showing that average delay does not grow with N is recently considered for symmetric systems in =-=[16]-=-. Specifically, work in [16] extends the results in [15] to show that average delay under an optimal algorithm in a system with symmetric Poisson traffic and 2N symmetric links is less than or equal t... |

24 | Opportunistic power scheduling for dynamic multiserver wireless systems - Lee, Mazumdar, et al. - 2006 |

22 |
Ajmone Marsan, “Bounds on Average Delays and Queue Length Averages and Variances in Input Queued and Combined Input/Output Queued Cell-Based Switches
- Leonardi, Mellia, et al.
- 2003
(Show Context)
Citation Context ...revious O(N/(1 − ρ)) bound in [7], it has a slightly worse asymptotic in ρ. Much work in the area of dynamic scheduling is developed for computer networks and switching systems, including work in [23]=-=[24]-=-[25][26] that uses Lyapunov stability theory. The work in [24] considers max-weight-match (MWM) scheduling in an N ×N packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that a... |

14 |
Multiaccess and fading in communication networks
- Yeh
- 2001
(Show Context)
Citation Context ...nce Foundation grant OCE 0520324, the DARPA IT-MANET program. and identical channel probabilities for each link, the LCQ policy minimizes average delay. This delay optimality result is generalized in =-=[4]-=- [10], where a delay optimal policy is developed for selecting transmission rates within the polytope capacity region associated with the Gaussian multiple access channel, and in [14] where generaliza... |

12 | Maximal matching scheduling is good enough
- Shah
- 2003
(Show Context)
Citation Context ...packet switch with i.i.d. traffic (such as Bernoulli or Poisson), and shows that average delay is no more than O(N/(1 − ρ)). Various methods of queue groupings are used with Lyapunov functions in [26]=-=[27]-=-[28] to achieve low complexity scheduling. While [26][27][28] does not primarily focus on delay, it is interesting to note that if an N × N switch is half loaded (ρ < 1/2) with independent Bernoulli o... |

9 |
Dynamic routing to parallel time-varying queues with applications to satellite and wireless networks
- Neely, Modiano, et al.
- 2002
(Show Context)
Citation Context ... {1, . . . , N}. B. The Single-Queue Lower Bound A simple lower bound on the average backlog (and hence, by Little’s Theorem [30], average delay), can be obtained by using the multiplexing inequality =-=[31]-=-. Specifically, the multiplexing ∑ inequality states that the total queue backlog N i=1 Qi(t) in a system of N queues described by (1) is greater than or equal to the backlog in a corresponding single... |

7 | A delay analysis for opportunistic transmission in fading broadcast channels
- Sharif, Hassibi
- 2005
(Show Context)
Citation Context ...us work in the area of wireless scheduling is found in [5][8][9] for systems with an infinite backlog of data, and a clearing problem in a system with N links and a fixed amount of data is treated in =-=[11]-=-. Stable scheduling and queueing is considered for satellite, wireless, and ad-hoc mobile systems in [1][2][3][6][7][12][13]. The work in [6] develops delay optimality results in the limit as the syst... |

7 |
Logarithmic delay for n×n packet switches under cross-bar constraint
- Neely, Modiano, et al.
- 2007
(Show Context)
Citation Context ...h the Lyapunov delay technique of [26] can be used to show that average delay is c/(1 − 2ρ) under maximal match scheduling. However, this result does not seem to extend to cases when ρ > 1/2. Work in =-=[32]-=- uses a simple frame-based algorithm for an N × N switch to show it is possible to achieve an average delay of c log(N)/(1 − ρ) 2 , for any value ρ < 1. Our results in the present paper parallel our p... |

3 | Logarithmic delay for n × n packet switches
- Neely, Modiano
- 2004
(Show Context)
Citation Context ...the Lyapunov delay technique of [24] can be used to show that average delay is O(1/(1 − ρ)) under maximal match scheduling. However, this result does not seem to extend to cases when ρ > 1/2. Work in =-=[29]-=- uses a simple framebased algorithm for an N × N switch to show it is possible to achieve an average delay of O(log(N)/(1 − ρ) 2 ), for any value ρ < 1. Our results in the present paper parallel our p... |

1 | Tsitsiklis. Transmission scheduling for multi-channel satellite and wireless networks
- Ganti, Modiano, et al.
- 2002
(Show Context)
Citation Context ...is generalized in [4] [10], where a delay optimal policy is developed for selecting transmission rates within the polytope capacity region associated with the Gaussian multiple access channel, and in =-=[14]-=- where generalizations to multi-server systems are considered. However, these delay optimality results hold only in cases when the system exhibits perfect symmetry in traffic rates and channel statist... |