## Statistical service assurances for traffic scheduling algorithms (2000)

Venue: | IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. SPECIAL ISSUE ON INTERNET QOS |

Citations: | 66 - 17 self |

### BibTeX

@ARTICLE{Boorstyn00statisticalservice,

author = {Robert Boorstyn and Almut Burchard and Jörg Liebeherr and Chaiwat Oottamakorn},

title = {Statistical service assurances for traffic scheduling algorithms},

journal = {IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. SPECIAL ISSUE ON INTERNET QOS},

year = {2000},

volume = {18}

}

### Years of Citing Articles

### OpenURL

### Abstract

Network services for the most demanding advanced networked applications which require absolute, per-flow service assurances can be deterministic or statistical. By exploiting statistical properties of traffic, statistical assurances can extract more capacity from a network than deterministic assurances. In this work we consider statistical service assurances for traffic scheduling algorithms. We present functions, so-called effective envelopes, which are, with high certainty, upper bounds of multiplexed traffic. Effective envelopes can be used to obtain bounds on the amount of traffic on a link that can be provisioned with statistical service assurances. We show that our bounds can be applied to a variety of packet scheduling algorithms. In fact, one can reuse existing admission control functions for scheduling algorithms with deterministic assurances. We present numerical examples which compare the number of ows with statistical assurances that can be admitted with our effective envelope approach to those achieved with existing methods.

### Citations

1680 | A generalized processor sharing approach to flow control in integrated services networks: The multiple node case
- Parekh, Gallager
- 1994
(Show Context)
Citation Context ...traffic pattern used in [15] is a periodic on–off source, which is known to maximize the overflow probability in a bufferless multiplexer. In [14], the solution approach of [15] is applied to the GP=-=S [29]-=- scheduling algorithm. The work of [15] has been extended by LoPresti, Zhang, Towsley, and Kurose [26] and by Rajagopal, Reisslein, and Ross [31]. The question of the adversarial traffic pattern at a ... |

636 | A scheme for real-time channel establishment in wide-area networks - Ferrari, Verma - 1990 |

617 | Integrated services in the internet architecture: an overview
- Braden, Clark, et al.
- 1994
(Show Context)
Citation Context ... on the randomness of flows are quite general. Note that we do not require ergodicity. • The type of traffic regulators most commonly used in practice are leaky buckets with a peak rate enforcer [1]=-=, [4]-=-. Here, traffic from flow is characterized by three parameters with a deterministic envelope given by where is the peak traffic rate, is the average traffic rate, and is a burst size parameter. We wil... |

557 |
A calculus for network delay, part I: Network elements in isolation
- Cruz
- 1991
(Show Context)
Citation Context ...ther deterministic or statistical. A deterministic service [16] guarantees that all packets from a flow satisfy given worst-case end-to-end delay bounds and no packets are dropped in the network [6], =-=[9]-=-. A deterministic service provides the highest level of QoS assurance, however, it leaves a significant portion of network resources on the average unused [37]. A statistical service [16] makes probab... |

510 | Service disciplines for guaranteed performance service in packet-switching networks
- ZHANG
- 1995
(Show Context)
Citation Context ...ces, the results for EDF in a statistical environment may still serve as a benchmark for other scheduling algorithms. The results in this paper can also be applied to rate-based scheduling algorithms =-=[39]-=-. If such algorithms are rate-proportional, the derivations of statistical bounds with effective envelopes are quite simple [24]. The discussions in this paper only consider a single node. Since, in a... |

301 | A calculus for network delay, part ii: Network analysis - Cruz - 1991 |

210 | Quality of service guarantees in virtual circuit switched networks - Cruz - 1995 |

174 | queue length, and delay of of deterministic and stochastic queueing networks
- Chang, “Stability
- 1994
(Show Context)
Citation Context ...be either deterministic or statistical. A deterministic service [16] guarantees that all packets from a flow satisfy given worst-case end-to-end delay bounds and no packets are dropped in the network =-=[6]-=-, [9]. A deterministic service provides the highest level of QoS assurance, however, it leaves a significant portion of network resources on the average unused [37]. A statistical service [16] makes p... |

165 | Efficient network QoS provisioning based on per node traffic shaping
- Georgiadis, Guérin, et al.
- 1996
(Show Context)
Citation Context ...d. The EDF algorithm was selected since it is known to be optimal for a deterministic service, in the sense that it can provide, among all scheduling algorithms, the highest level of delay assurances =-=[17]-=-, [25]. Even though optimality of EDF scheduling has not been proven for statistical QoS assurances, the results for EDF in a statistical environment may still serve as a benchmark for other schedulin... |

155 | Exact Admission Control in Networks with Bounded Delay Services
- Liebeherr, Wrege, et al.
- 1994
(Show Context)
Citation Context ... for a deterministic service [6], [9]. In fact, we show that one can reuse admission control conditions derived for various scheduling algorithms in the context of a deterministic service, e.g., [9], =-=[25]-=-, [40]. This is encouraging since only few results are available on statistical multiplexing of adversarial traffic which can consider nontrivial scheduling algorithms, e.g., [14], [21]. Let us make a... |

150 | A new approach for allocating buffers and bandwidth to heterogeneous, regulated traffic in an ATM node
- Elwalid, Mitra, et al.
- 1995
(Show Context)
Citation Context ...tion of traffic sources, recent research on statistical QoS has attempted to define statistical services without making assumptions on properties of traffic sources. Starting with the seminal work in =-=[15]-=-, researchers have investigated the statistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator... |

143 |
On computing per-session performance bounds in high-speed multi-hop computer networks
- Kurose
- 1992
(Show Context)
Citation Context ...s probabilistic bounds for delay violations at an EDF scheduler, assuming that the arrival distribution of traffic is known. Specific results are derived for on–off traffic as assumed in [15]. Kuros=-=e [23]-=- explores bounds on the distribution of the delay and buffer occupancy of a flow in a network environment by characterizing the traffic on a flow by a family of random variables, which describe the tr... |

142 | Rate-controlled service disciplines
- Zhang, Ferrari
- 1994
(Show Context)
Citation Context ... deterministic service [6], [9]. In fact, we show that one can reuse admission control conditions derived for various scheduling algorithms in the context of a deterministic service, e.g., [9], [25], =-=[40]-=-. This is encouraging since only few results are available on statistical multiplexing of adversarial traffic which can consider nontrivial scheduling algorithms, e.g., [14], [21]. Let us make a few r... |

125 | Performance and stability of communication networks via robust exponential bounds
- Yaron, Sidi
- 1993
(Show Context)
Citation Context ...erved in a fluid-flow fashion at an allocated rate. A key difference to our work is an assumption that there exists an a priori bound on the moment generating function of the arrivals. Yaron and Sidi =-=[38]-=- prove that if the incoming flows to a multiplexer satisfy exponentially bounded burstiness constraints, then the output of the multiplexer has exponentially bounded burstiness. The work was recently ... |

114 |
Broadband Integrated Networks
- Schwartz
- 1996
(Show Context)
Citation Context ...ity of service networks is extensive, and so a full discussion is beyond the scope of this paper. Excellent reviews of the state of the art of statistical multiplexing can be found in [22], [34], and =-=[35]-=-. Here, we discuss only two groups of prior work on statistical multiplexing which we regard as particularly relevant to this paper. The first group studies the statistical multiplexing gain of statis... |

109 | Deterministic delay bounds for VBR video in packet-switching networks: Fundamental limits and practical tradeoffs
- Wrege, Knightly, et al.
- 1996
(Show Context)
Citation Context ...o packets are dropped in the network [6], [9]. A deterministic service provides the highest level of QoS assurance, however, it leaves a significant portion of network resources on the average unused =-=[37]-=-. A statistical service [16] makes probabilistic service assurances, for example, of the form where is generally small, e.g., . By allowing a fraction of traffic to violate its QoS, one can significan... |

105 | Admission control for statistical QoS: theory and practice
- Knightly, Shroff
(Show Context)
Citation Context ... order to obtain a useful estimate for the distribution of the supremum. One way to provide a theoretical justification for the assumption in (64) is to assume that arrivals follow a Gaussian process =-=[22]-=-. Other works on statistical QoS have supported the assumption in (64) with numerical examples [7], [20], [21], [23]. Recall from the definition of the local effective envelope that implies . Then, wi... |

96 | queue length, and delay of deterministic and stochastic queueing networks - Stability - 1994 |

77 |
Extreme value theory in engineering
- Castillo
- 1988
(Show Context)
Citation Context ...can rewrite (63) as (63) (64) (65) Remark: The assumption in (64) does not hold in general, since the right-hand side is an upper bound for the left-hand side. Note that standard extreme-value theory =-=[5]-=- is not immediately applicable to the left-hand side of (64), since the supremum is taken over a family of random variables indexed by the continuous parameter . Thus, one must consider the correlatio... |

66 | A generalized processor sharing approach to ‡ow control inintegrated services networks: the single-node case - Parekh, Gallager - 1993 |

61 | Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes
- Elwalid, Mitra
- 1999
(Show Context)
Citation Context ... service, e.g., [9], [25], [40]. This is encouraging since only few results are available on statistical multiplexing of adversarial traffic which can consider nontrivial scheduling algorithms, e.g., =-=[14], -=-[21]. Let us make a few remarks on the scope of this paper. The scheduling algorithms considered here are first-come–firstserved (FCFS), static priority (SP), and earliest-deadline-first (EDF) (see ... |

61 | Source time scale and optimal buffer/bandwidth tradeoff for regulated traffic in an ATM node
- LoPresti, Zhang, et al.
- 1997
(Show Context)
Citation Context ...exing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g., by a leaky bucket [13]–[15], [18], [19], [21]=-=, [26], -=-[27], [31]–[33]. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, but otherwise adversarial traffic flo... |

59 | Providing end-to-end statistical performance guarantees with bounding interval dependent stochastic models
- Zhang, Knightly
- 1994
(Show Context)
Citation Context ...h describe the traffic over time intervals. For FIFO scheduling, Kurose also provides bounds on the output of a node, and, thus, can obtain bounds for networks with multiple nodes. Zhang and Knightly =-=[41]-=- extend this work for specific arrival distributions and scheduling algorithms. Both [23] and [41] calculate the arrival distribution of aggregate sources directly, without resorting to large deviatio... |

58 | Stochastically bounded burstiness for communication networks
- Starobinski, Sidi
(Show Context)
Citation Context ...if the incoming flows to a multiplexer satisfy exponentially bounded burstiness constraints, then the output of the multiplexer has exponentially bounded burstiness. The work was recently extended in =-=[36]-=- to more general bounding functions. Cruz [12] computes probabilistic bounds on the delay and backlog at a scheduler, assuming that probabilistic bounds on traffic arrivals and service curves [11] are... |

53 | Inter-class resource sharing using statistical service envelopes
- Qiu, Knightly
- 1999
(Show Context)
Citation Context ...ctions. Cruz [12] computes probabilistic bounds on the delay and backlog at a scheduler, assuming that probabilistic bounds on traffic arrivals and service curves [11] are available. Qiu and Knightly =-=[30]-=- extend this approach and develop a framework for statistical service envelopes. Andrews [2] provides probabilistic bounds for delay violations at an EDF scheduler, assuming that the arrival distribut... |

52 | H-BIND: A new approach to providing statistical performance guarantees to VBR traffic
- Knightly
- 1996
(Show Context)
Citation Context ... specific arrival distributions and scheduling algorithms. Both [23] and [41] calculate the arrival distribution of aggregate sources directly, without resorting to large deviations results. Knightly =-=[20]-=-, [21] characterizes flow arrivals using first and second moment information on the sources. The notion of a rate-variance envelope is introduced to describe the variance ofsBOORSTYN et al.: STATISTIC... |

52 | Enforceable quality of service guarantees for bursty traffic streams - Knightly - 1998 |

42 |
Deterministic rule based traffic descriptors for broadband ISDN: worst case behavior and connection acceptance control
- Doshi
- 1994
(Show Context)
Citation Context ...gated the statistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g., by a leaky bucket =-=[13]–[-=-15], [18], [19], [21], [26], [27], [31]–[33]. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, but othe... |

38 | Measurement-based usage charges in communication networks - Courcoubetis, Kelly, et al. |

37 | Probabilistic end-to-end delay bounds for earliest deadline first scheduling
- Andrews
(Show Context)
Citation Context ...ming that probabilistic bounds on traffic arrivals and service curves [11] are available. Qiu and Knightly [30] extend this approach and develop a framework for statistical service envelopes. Andrews =-=[2] p-=-rovides probabilistic bounds for delay violations at an EDF scheduler, assuming that the arrival distribution of traffic is known. Specific results are derived for on–off traffic as assumed in [15].... |

36 | Random Variables, and Stochastic Processes, 3rd ed - Papoulis, Probability - 1991 |

35 |
The ATM Forum Traffic Management Specification Version 4.0. ftp://ftp.atmforum.com/pub/approved-specs/af-tm-0056.000.ps
- Forum
- 1996
(Show Context)
Citation Context ...s and on the randomness of flows are quite general. Note that we do not require ergodicity. • The type of traffic regulators most commonly used in practice are leaky buckets with a peak rate enforce=-=r [1]-=-, [4]. Here, traffic from flow is characterized by three parameters with a deterministic envelope given by where is the peak traffic rate, is the average traffic rate, and is a burst size parameter. W... |

30 | Packet multiplexers with adversarial regulated traffic
- Rajagopal, Reisslein, et al.
- 1998
(Show Context)
Citation Context ...y only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g., by a leaky bucket [13]–[15], [18], [19], [21], [26], [27]=-=, [31]��-=-�[33]. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, but otherwise adversarial traffic flows at a netw... |

23 |
Eds.). Broadband Network Traffic: Performance Evaluation and Desgin of Broadband Multiservice Networks
- Roberts, Mocci, et al.
- 1996
(Show Context)
Citation Context ...ng in quality of service networks is extensive, and so a full discussion is beyond the scope of this paper. Excellent reviews of the state of the art of statistical multiplexing can be found in [22], =-=[34]-=-, and [35]. Here, we discuss only two groups of prior work on statistical multiplexing which we regard as particularly relevant to this paper. The first group studies the statistical multiplexing gain... |

21 | A central-limit-theorem-based approach for analyizing queue behvior in high-speed network
- Choe, Shroff
- 1998
(Show Context)
Citation Context ...etical justification for the assumption in (64) is to assume that arrivals follow a Gaussian process [22]. Other works on statistical QoS have supported the assumption in (64) with numerical examples =-=[7]-=-, [20], [21], [23]. Recall from the definition of the local effective envelope that implies . Then, with Lemma 1(a) and assuming that (64) holds with equality, we have that a class- arrival has a dead... |

21 | Guaranteeing statistical QoS to regulated traffic: The multiple node case - Reisslein, Ross, et al. - 1998 |

18 | ATM Forum Tra c Management Speci cation Version 4.0 - Forum - 1996 |

17 | calculus for network delay, part ii: Network analysis - “A - 1991 |

17 | Extremal shape-controlled traffic patterns in high-speed networks
- Kesidis, Konstantopoulos
- 1997
(Show Context)
Citation Context ...tatistical multiplexing gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g., by a leaky bucket [13]–[15]=-=, [18], -=-[19], [21], [26], [27], [31]–[33]. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, but otherwise adver... |

17 | Tradeoffs in Designing Networks with End-to-End - Patek, Liebeherr, et al. |

15 | A new Approach for Allocating Bu ers and Bandwidth to Heterogeneous, Regulated Tra c in ATM node - Elwalid, Mitra, et al. - 1995 |

10 | E cient network QoS provisioning based on per node tra c shaping - Georgiadis, Guerin, et al. - 1996 |

8 | Source time scale and optimal buer/bandwidth trade-o for regulated trac in an ATM node - LoPresti, Zhang, et al. - 1997 |

5 | Statistical multiplexing gain of link scheduling algorithms in QoS networks
- Boorstyn, Burchard, et al.
- 1999
(Show Context)
Citation Context ...e flows in the classes are as follows: Class Peak Rate Mean Rate Burst Size (Mb/s) (Mb/s) (bits) The parameters are selected so as to match (approximately) the examples presented in [15] and [31]. In =-=[3]-=- we present additional experiments, including experiments with MPEG video traces. In this section we present three sets of examples. The first two examples only include results for Class 1 traffic. A.... |

5 | On-off sources and worst case arrival patterns of the leaky bucket
- Oechslin
- 1997
(Show Context)
Citation Context ...gain by only assuming that flows are statistically independent, and that traffic from each flow is constrained by a deterministic regulator, e.g., by a leaky bucket [13]–[15], [18], [19], [21], [26]=-=, [27], -=-[31]–[33]. In this paper we attempt to provide new insights into the problem of determining the multiplexing gain of statistically independent, regulated, but otherwise adversarial traffic flows at ... |

5 | Deterministic rule based tra c descriptors for broadband ISDN: Worst case behavior and concept equivalent bandwidth - Doshi - 1993 |

4 | Broadband network tra c: performance evaluation and design of broadband multiservice networks: final report of action cost 242 - Roberts, Mocci, et al. |

2 | Extremal shape-controlled tra c patterns in high-speed networks - Kesidis, Konstantopoulos |

2 | Extremal tra c and worstcase performance for queues with shaped arrivals - Kesidis, Konstantopoulos - 1998 |

2 | Guaranteeing statistical QoS to regulated tra c: The multiple node case - Reisslein, Ross, et al. - 1998 |