Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04Q—SELECTING
  • H04Q11/00—Selecting arrangements for multiplex systems
  • H04Q11/04—Selecting arrangements for multiplex systems for time-division multiplexing
  • H04Q11/0428—Integrated services digital network, i.e. systems for transmission of different types of digitised signals, e.g. speech, data, telecentral, television signals
  • H04Q11/0478—Provisions for broadband connections
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L12/00—Data switching networks
  • H04L12/28—Data switching networks characterised by path configuration, e.g. LAN [Local Area Networks] or WAN [Wide Area Networks]
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L12/00—Data switching networks
  • H04L12/54—Store-and-forward switching systems 
  • H04L12/56—Packet switching systems
  • H04L12/5601—Transfer mode dependent, e.g. ATM
  • H04L2012/5629—Admission control
  • H04L2012/5631—Resource management and allocation
  • H04L2012/5632—Bandwidth allocation
  • H04L2012/5635—Backpressure, e.g. for ABR

Definitions

• the present invention relates generally to a packet switching network, and in particular, to a fair flow controlling method.
• Packet switching networks include ATM (Asynchronous Transfer Mode) networks and the Internet.
• a fair flow control has significant effects in the information transmission over a packet switching network.
• a fair flow control of the ATM networks is related to the ABR (Available Bit Rate) service.
• the ATM layer provides the following four services: CBR (Constant Bit Rate), VBR (Variable Bit Rate), UBR (Unspecified Bit Rate), and ABR.
• CBR Constant Bit Rate
• VBR Variable Bit Rate
• UBR Unspecified Bit Rate
• ABR Access Bit Rate
• the source dynamically changes its bit rate within the available bandwidth from the network to adapt the changing network conditions when transmitting the data.
• the ABR service was introduced to the ATM network in order to support data applications that were not efficiently supported by a guaranteed bandwidth service, such as the VBR service. For details, see S. Sathaye, ATM forum Traffic Management Specification, Version 4.0, Feb. 1996, F. Bonomi and K. W. Fendick "The Rate-Based Flow Control Framework for the Available Bit Rate ATM Service", IEEE Network, vol. 9, no. 2, pp.
• the network has to work comply with a certain condition satisfying the predefined cell loss requirements, time-varying tolerance requirements, and cell delays. Due to these characteristics, the network has to modify their data transfer rates according to the network loading conditions.
• the notion of elastic traffic services was introduced in which the data transfer rates are adjusted based on the bandwidth available from the network.
• a representative example of the elastic traffic services is the ABR service of ATM networks.
• the ABR service does not require a complex traffic characterization and call admission control, respectively, at the source and at the switches Due to this simplicity, it has been expected that the implementation and the deployment of the ABR service would be much easier than those of the bandwidth-guaranteed services, i e CBR or VBR service In reality, however, the implementation of ABR-capable switches appears to be much more difficult than originally expected
• the difficulty mainly lies in the designing of a simple, scalable, and stable ABR flow algorithm, more specifically an ER (Explicit Rate) allocation algorithm in an asynchronous and distributed network environment
• the ATM forum has selected a closed-loop rate-based approach for the ABR flow control
• the closed-loop rate-based flow control approach uses feedback information from the network to control the data rate at which each source can transmit a number of cells into the network
• the feedback information is conveyed to the source through a specific control cell known as a resource management (RM) cell
• RM resource management
• EFCI Explicit Forward Congestion Indication
• RR Relative Rate
• ER marking at least one of which has to be implemented on a switch for the rate-based flow control
• r[k] is the ER calculated by the switch at the discrete time k
• q[k] is per-class ABR queue length at the time k
• qT is a target queue length
• ⁇ i and ⁇ j are controller gains
• ⁇ max is the largest RTD of an ABR VC
• I is an arbitrary constant greater than 0
• the ER allocation algorithm (3) is disclosed as U S Patent No 5,864,538 entitled “First-Order Rate-Based Flow Control with Adaptive Queue Threshold for ATM Networks", January 26, 1999
• a common drawback of the algorithms (2) and (3), as compared to the algorithm (1), is that unless the controller gains and the queue length threshold are properly chosen according to the instantaneous knowledge on the bandwidth available to ABR traffic and the fraction of the available bandwidth utilized by remotely bottlenecked VCs, the ABR queue length can converge to zero which is undesirable because, at this equilibrium point, the link cannot be fully utilized
• the remotely bottlenecked VCs cannot fairly share the link since the phenomenon of bottle neck occurs at another link if the transmission rates of the VCs are not limited by their PCRs (Peak Cell Rates). In contrast, if the algorithm (1) is applied, there exists no such undesirable equilibrium point.
• an object of the present invention to provide a method of guaranteeing the maximal link utilization and minimal cell loss regardless of RTDs in an ABR loop
• ABR queue size requirements by ensuring asymptotical stabilization of the ABR queues
• the above object of the present invention can be achieved by providing a fair flow controlling method in a packet switching network
• the packet switching network includes a plurality of nodes and each node is connected to a plurality of sources which transmits/receives data, and includes a data queue related with a current queue length and a target queue length for storing data received from the sources
• each node estimates the number of locally bottlenecked VCs using the ER and the MCR to be guaranteed of a corresponding source
• the node allocates an
• ER to each source based on the difference between the current queue length and the target queue length of the node, the derivative of the current queue length, and the estimated number of the locally bottlenecked VCs, then conveys the ER to each source through a feedback signal
• FIG 1 illustrates a network configuration to provide the ABR service
• FIG 2 illustrates fields in an RM cell
• FIG 3 schematically illustrates a switch fabric for the ABR service having I/O ports connected to I/O cards
• FIG 4 is a detailed block diagram of an I/O card shown in FIG 3,
• FIG 5 is a block diagram of an ABR service engine according to the preferred embodiment of the present invention.
• FIG 6 illustrates a network model with a node of interest
• FIG 7 is a graph showing a stable region with respect to U and V according to the preferred embodiment of the present invention
• FIG 8 illustrates an asymptotic decay rate as a function of U and V
• FIG 9 illustrates queue length thresholds for ER marking and RR marking
• FIG 10 illustrates a peer to peer configuration
• FIG 13 illustrates a parking lot configuration
• FIGs 14A to 14F illustrate simulation results in the parking lot configuration with ER marking only and no VBR background traffic
• FIG 14C shows a queue length at a switch SW3
• FIG 14D shows a queue length at a switch SW4
• FIG 14E shows the estimated number
• FIG 14F shows the estimated number
• FIG 1 illustrates a network configuration for implementing the ABR service
• a network 2 for providing the ABR service includes a plurality of nodes 4, 6, 8, and 10
• the nodes conceptually represent switches and will be referred to as switches hereinafter
• Each switch is connected to a plurality of sources
• the switch 4 is connected to sources A and C as indicated by reference numerals 12 and 14
• the switch 8 is connected to sources B and D as indicated by reference numerals 16 and 18
• Each source transmits/receives data through the switch 4 or 8 connected to the source
• Data transmitted from the source reaches a destination through a so-called VC path having a plurality of nodes
• VC path having a plurality of nodes
• data from the source A 12 reaches the destination, the source B 16, through a VC path having the switches 4, 6, and
• RM Resource Management
• FIG 1 RMc denotes an RM cell While RM cells are generated in the sources 12, 14, 16, and 18 or the switches 4, 6, 8, and 10, the following description is confined to a source-generated RM cell A source-generated RM cell is transmitted to a destination through the switches
• the transmission direction of the cell is forward Upon receiving the forward RM cell, the destination returns the cell (backward) back to the source
• reference numerals 12 and 14 denote sources
• reference numerals 16 and 18 denote destinations With respect to the sources and destinations, the forward and backward directions are defined as shown
• the switches 8, 6, and 4 write their allowed bandwidth information in the backward RM cell
• the source 12 or 14 adapts its rate according to the changing network conditions based on the received bandwidth information
• An RM cell contains information that includes fields of CCR (Current Cell Rate),
• an S-R (Source-Receive) field provides information related to a source and a destination information
• the CCR field is set by the source to its current ACR (Allowed Cell Rate) when the source generates the RM cell
• the MCR field indicates the minimum bandwidth allocated to each VC when the source generates the RM cell ER is an available bandwidth written in a backward source-generated RM cell by the ABR service engine of a switch as the RM cell passes through the switch Only if a calculated available bandwidth of the ABR service engine is less than the existing available bandwidth, the former value is written in the ER field
• the source writes its PCR in the ER field when it generates the RN cell CI and NI are fields used to control RR CI notifies the source that the network is much congested and thus the bandwidth of the source is
• a switch calculates a bandwidth available for the ABR service and writes the available bandwidth information in a backward RM cell, using a switch algorithm What is intended from the switch algorithm is to obtain a bandwidth allowable to a corresponding VC by the switch This available bandwidth is conveyed to the source so that the source adapts its rate to provide the ABR service reliably
• a switch fabric 20 has I/O ports each connected to an I O port card 22 in each switch shown in FIG 1
• Each I/O port card includes an I/O buffer management unit 30, an ABR service engine 32, and an output interface 34, as shown in FIG 4
• the I O buffer management unit 30 is connected to the switch fabric 20 and responsible for I/O queuing
• the I/O buffer management unit 30 includes ABR queues 36
• the ABR service engine 32 implements an ABR algorithm and its related operations for the ABR service while an RM cell is passing through the ABR engine 32 according to the embodiment of the present invention
• the output interface 34 acts as a user network interface at the ATM layer
• FIG 5 is a block diagram of the ABR service engine 32 shown in FIG 4 With reference to FIG 5, the ABR service engine 32 is comprised of an EFCI marker 40, a
• the EFCI marker 40 marks an EFCI bit in an input forward data cell to indicate the EFCI congestion
• a queue read signal is generated when a cell is removed from a queue and a queue write signal is generated when a new cell enters the queue
• the average queue calculator 46 increases a queue instantaneous variable by one, and upon receipt of the queue read signal, it decreases the queue instantaneous variable by one, to calculate an average queue length within a predetermined period interval for the ER computation
• the average queue calculator 46 feeds the average queue length q[k] to the ER engine 44
• the average queue calculator 46 decides as to whether the EFCI congestion has occurred using the queue read signal and the queue write signal and in case of the EFCI congestion, it outputs an EFCI congestion signal EFCI CG to the EFCI marker 40
• the average queue calculator 46 also outputs a signal CG representative of "congested" condition and a signal VCG representative of "very congested" condition
• estimation unit 42 estimates the number of locally bottlenecked VCs by reading CCR and MCR from an RM cell and comparing CCR-MCR with a periodically calculated ER r(t) Interval, W, at which the estimated value
• is provided to the ER engine 44
• the ER engine 44 updates the ER through a periodical ER calculation and outputs the latest ER r(t) to the backward RM cell writer 48 upon arrival of a backward RM cell
• the backward RM cell writer 48 writes r(t) in the ER field of the backward RM cell More specifically, the backward RM cell writer 48 compares the ER of the received RM cell with r(t) + the MCR of the RM cell (r(t)+m ⁇ ) and writes r(t)+m ⁇ in the RM cell only when r(t)+m ⁇ is less than the ER of the RM cell.
• the backward RM cell writer 48 writes a binary logic state bit in the NI and CI fields of the RM cell according to the signals CG and VCG received from the average queue calculator 46, for control of RR
• FIG 16 is a flowchart illustrating an ER allocation control operation in the ABR service engine
• estimation unit 42 estimates Q in step 100 and the ER engine 44 updates ER through a periodical calculation in step 102
• the ABR service engine 32 proceeds to step 106, otherwise, it returns to step 100
• the backward RM cell writer 48 reads the latest ER r(t) from the ER engine 44 and the MCR mi from the received RM cell
• the backward RM cell writer 48 calculates an ER allocation value ⁇ (t) for VCi (an ⁇ th VC) by r(t)+m ⁇ in step 108 and writes ⁇ (t) in the ER field of the backward RM cell in step 110
• the purpose of the switch algorithm suggested in the present invention is to converge the AVR queue 36 to a target queue length qT and maintain a queue length at a steady state at the target queue length qT, which implies that the input traffic is equal to the output traffic of the ABR queue 36 A transient period is generated in the process of achieving the target queue length qT In case the input traffic is momentarily greater than the output traffic, the ABR queue 36 is overloaded As a result, unexpected cell loss might occur Accordingly, a switch algorithm is implemented considering the buffer capacity and queue length variation of the ABR queue 36 in the embodiment of the present invention
• r(t) is an ER calculated by the ER engine
• r(t) is the derivative of r(t)
• Q is the set of locally bottlenecked VCs
• is the cardinality of Q
• q(t) is the length of the ABR queue 36 at a time t
• a and B are controller gains that are varied depending on the length of the ABR queue 36 for asymptotic stability in the embodiment of the present invention
• q(t) is the derivative of q(t), which will be described in relation with Eq (21) and Eq (23)
• the control-theoretic ER allocation algorithm (4) of the present invention achieves MAX-MIN fair rate allocation according to the principle as described below
• An identical ER (common ER) is allocated to all VCs, based on Eq (4), sharing the same link
• the minimum allocated ER in the path is conveyed to a source through an RM cell and the source transmits data at the minimum ER
• the ABR queue 36 will experience time delay and the delay will be decayed
• the switch increases the common ER until the ABR queue 36 reaches the target queue length qT in the algorithm (4) Therefore, each locally bottlenecked VC can get a fair share of the bandwidth that is not used by remotely bottlenecked VCs
• the algorithm (4) can be approximated to the following discrete time algorithm when it applies in reality
• the queue length control is a primary concern
• the fair rate allocation is a by-product of the queue length control
• the queue length control is supplementary
• the ER allocation algorithm of the present invention will be modeled mathematically and it will be shown that the ER allocation algorithm guarantees an MCR required by each source and at the same time satisfies the MAX-MIN fairness
• FIG 6 illustrates a network model with a node of interest
• a plurality of VCs are matched with a plurality of corresponding sources, VCi 54 to source l 50 and VCj 56 to source j 52
• Reference numeral 36 denotes the ABR queue
• qT is the target queue length
• ⁇ denotes the available bandwidth of a link shared by the plurality of VCs ⁇ f and ⁇ b are forward and backward path delays, respectively, in VCi 54
• the sum of ⁇ f and ⁇ b is the RTD ⁇ i of VCi 54 ⁇ j f and ⁇ j b are forward and backward path delays, respectively, in VCi 56
• the sum of ⁇ j f and ⁇ j b is the RTD ⁇ j of VCi 56
• the network model is analyzed based on the following assumptions
• a 1 Traffic is viewed as a deterministic fluid flow, and the network queuing process and the flow control mechanism are continuous in time This assumption enables the closed-loop system to be modeled by a differential equation
• the RTD ⁇ i of VCi 54 is the sum of the forward path delay ⁇ i f and the backward path delay ⁇ i b , which includes propagation, queuing, transmission, and processing time
• the RTD is assumed to be constant
• ⁇ i(t) and ri(t) respectively denote the rate at which source i transmits data at source time t and the ER of VCi computed by the node of interest at node time t
• ⁇ i(t) and pi(t) respectively denote the latest minimum of ERs allocated to VCi by the nodes along the VCi's path, except the one allocated by the node of interest and the PCR constraint of VCi
• ⁇ i(t) min[ri(t- ⁇ i b ), bi(t), pi], Vi e N (6),
• N is the set of all the VCs whose route includes the node of interest
• This model implies that source i 54 transmits data at the smallest value among an ER allocated by the node of interest before the backward path delay ⁇ i b , ri(t— ⁇ i ), a minimum ER on the route except the node of interest, bi(t), and the PCR of the VC, pi
• the ER allocation algorithm is a distributed algorithm which runs at each switch based on the current network state including the queue length q(t), the derivative of the queue length, q(t) , and the estimate of the number of locally bottlenecked VCs, Q , given by
• A, B > 0 and mi denotes the MCR which the node is required to guarantee during the entire life of VCi It is assumed that mi ⁇ pi, Vi e N, and there exists a call admission control which guarantees the following condition
• the embodiment of the present invention is characterized in that the node keeps updating the common ER in the background "Background” calculation refers to the calculation of the common ER periodically regardless of the arrival of RM cells
• the benefit of the background calculation is that the latest common ER, r(t) that is preliminarily updated is directly provided upon arrival of an RM cell in the corresponding node
• the node that has updated the common ER, r(t) according to Eq (9) by background calculation, reads mi from the MCR field of a passing-by RM cell in VCi 54, calculates an ER ri(t) to be allocated to VCi 54 by adding mi to the latest common ER, r(t) in Eq (8), and writes ri(t) in the ER field of the RM cell
• Another notable feature of the ER allocation algorithm according to the embodiment of the present invention is the normalization of the controller gains, A and B according to the estimate of the number of locally bottlenecked VCs,
• the normalization is optional, that is, it is not absolutely necessary but it is recommended since, as it will be described in "(4) Principal Root and Asymptotic Decay Rate", it makes the asymptotic decay rate of the closed-loop system to be independent of the number of locally bottlenecked VCs
• remotely bottlenecked VC and locally bottlenecked VC are defined in the steady state for a given network loading
• Remotely bottlenecked VCs in a given link are defined as those VCs which cannot achieve their fair share at the given link because either their transfer rate is limited by their PCR or they represent bottlenecked at some other link in the path
• locally bottlenecked VCs at a link are defined as those VCs which achieve their fair share at the given link
• N-Q ⁇ i
• i e N and ais min[b ⁇ s, pi] ⁇ (12)
• the embodiment of the present invention has the following characteristics; and a result, Eq. (19) is obtained.
• ⁇ e ⁇ f w, ⁇ ⁇
• the ABR closed-loop system has a unique oscillation-free operating point at which the MAX-MIN fairness with NCR guarantee is achieved, and the queue length is equal to the target value qT no matter what the network loading is. That is, an equilibrium point is independent of the available bandwidth for the ABR traffic and the fraction of the available bandwidth utilized by remotely bottlenecked VCs including PCR-constrained VCs.
• a notable point about the embodiment of the present invention is that the ER allocation algorithm results in the unique equilibrium point but the computation is very simple.
• the ER algorithm requires q(t) and q(t) only, not any other measurement or monitoring result.
• used to normalize the gains A and B, is introduced to accelerate the convergence of the queue length to the target queue length and has little to do with the equilibrium point.
• the Benmohamed's algorithm in Eq. (1) also results in a unique system equilibrium point with the same properties as the ER allocation algorithm of the present invention but at the cost of high-degree implementation complexity. In contrast, if the algorithms in Eq. (2) and Eq.
• the closed-loop system possesses an equilibrium point that varies depending on the available bandwidth and the fraction of the available bandwidth utilized by the remotely bottlenecked VCs and can converge to zero at worst scenario.
• S. Chong, Nagarijan, and Y. T. Wang “Design Stable ABR Flow Control with Rate Feedback and Open-Loop Control: First-Order Control Case", Performance Evaluation, vol. 34, no. 4, pp. 189-206, 1998, S.
• Stepan' s criterion provides a way to construct the necessary and sufficient condition (see “Retarded Dynamical Systems Stability and Characteristic Functions", Longman Scientific & Technical, 1989)
• constructing such a condition in an explicit form is extremely complicated particularly for the case with a large number of heterogeneous RTDs
• FIG 7 illustrates a stable region with respect to U and V according to the embodiment of the present invention
• — is the asymptotic decay rate at which the original system tends to ⁇ a the equilibrium point
• — is the time constant of the original ⁇ closed-loop system, i e , the time it takes for a small perturbation around the equilibrium point to decrease by a factor of e l
• ⁇ and of are the asymptotic decay rate and the time constant of the normalized system
• FIG 8 illustrates the asymptotic decay rate ⁇ as a function of U and V
• the contour line at ⁇ corresponds to the boundary of the stable region shown in FIG 7
• the ER allocation algorithm expressed in Eq (8) and Eq (9) can be implemented at a switch in discrete time as follows Update the common ER periodically with a period T by
• r[k + l] [r[k] - ⁇ (q[k]- q[k - ⁇ ]) - ⁇ (q[k] - qy] A,B > 0 (34),
• a periodic averaging filter is used in order to obtain q[k] in the embodiment
• the ER update equation (34) corresponds to Eq (9) as T -> oo
• r(t) denotes the latest value, r[k+l], of the common ER, r[k], which is being updated periodically in the background according to the embodiment of the present invention
• the value of mi is available from the RM cell that has arrived or the per-VC MCR table being maintained in the switch and updated upon arrival or departure of an RM cell If it is determined that the value of mi is to be taken from the RM cell that has arrived, the per-VC MCR table and the access to it are no longer necessary Therefore, the only per-VC operation required in the ER allocation algorithm of the present invention is the addition in Eq (35)
• a j th RM cell arrives at a switch at a switch time t 1
• the j th RM cell happens to be an RM cell of VCi
• it carries the value ai(t J - ⁇ i f ) in the CCR field and the value mi in the MCR field
• the switch monitors the RM cell arrivals in a synchronous fashion over fixed length intervals of W seconds For an 1 th interval, the number of locally bottlenecked VCs can be approximated by bL . . .
• NRM+ V correct estimate of the number of locally bottlenecked VCs Based on this estimate for each interval, the recursive estimate is computed at the end of every interval by
• ⁇ is an averaging factor
• int[a] denotes the smallest positive integer greater than or equal to a
• saturation function sata[b] is defined as
• RR marking is applied in conjunction with ER marking
• the ER marking plays the major role to achieve the MAX-MIN fairness with MCR guarantee in an asymptotically stable manner whereas the RR marking plays a supplementary role to limit the transient overshooting of the queue length and hence minimize the transient cell loss
• FIG 9 illustrates the suggested design of the queue length thresholds for the ER plus RR marking
• qT is the target queue length
• qLT is the lowest queue length threshold for the ABR queue
• qHT is the highest queue length threshold for the ABR queue
• qT is related with ER marking
• qLT and qHT are related with RR marking
• qLT is a threshold from which the NI bit of a NI field is set
• qHT is one from which the CI bit of a CI field
• simulation results will be presented to verify the above-described analysis and demonstrate the excellent performance of the ER allocation algorithm according to the embodiment of the present invention
• the simulation model used is developed on the NIST ATM simulator platform
• the PCR value, the MCR value, the ICR value, and the arrival and departure times of the VCs are varied in order to investigate the impacts of the PCR-constrained sources, the difference in MCR and ICR, and the call activities on the network performance
• the theoretical fair rates satisfying the MAX-MIN fairness with MCR guarantee are calculated and the results are listed in Table 2 Referring to Table 2 and FIG 10, it is observed that the fair rate of each VC varies in time according to the arrivals and departures of the other VCs and that the sources sl l to slO are bottlenecked at the switch SW1, and the sources sl l to s20 are bottlenecked at the access by its PCR constraint
• the ABR sources si to s4 should transmit data at 36 1Mbps in 0-1 sec, 30Mbps in 2-3 sec, and 32 5Mbps in 3 ⁇ oo sec to be Max-MTN fair
• 32 data cells are generated between two adjacent forward RM cells
• FIGs 11A to 11D illustrate simulation results in the peer-to-peer configuration with ER marking only and without no VBR background traffic
• FIGs 12A to 12D illustrate simulation results in the peer-to-peer configuration with ER marking and VBR background traffic
• the transmission rates of the sources si to s4 and si 0 are equal to the common ER, r(t) computed by the switch SW1 since their MCR is 0Mbps, the transmission rates of the sources s5 to s9 are greater than the common ER, r(t) since their MCR is 10Mbps, and the sources sl l to s20 are PCR-constrained irrespective of their MCR values
• FIG 1 IC illustrates a queue length at the bottleneck node
• VBR background traffic With VBR background traffic the results are virtually unchanged as shown in FIGs 12A to 12D That is, the macroscopic (time-averaged) behavior is identical to that of the case with no VBR traffic disturbance
• the VBR background traffic was generated by a deterministic on/off source with the peak rate and the lengths of on and off periods are, respectively, 10Mbps, 20 ⁇ maxsecs, and 20 ⁇ maxsecs It is noted from FIGs 12A and 12B that the transmission rate of the sources (except the PCR-constrained sources) almost perfectly follows the on/off pattern of the VBR background traffic
• the on/off behavior of the VBR background traffic causes the repeated surges and drops of the ABR queue length
• the ER allocation algorithm according to the embodiment of the present invention, however, rapidly recovers the queue length to the target value as shown in FIG 12C
• FIGs 14A to 14F illustrate the simulation results with ER marking only and no VBR background traffic
• FIG 14C illustrates a queue length at the switch SW3,
• FIG 14D a queue length at the switch SW4,
• FIG 14E illustrates the estimate of the number of locally bottlenecked VCs,
• FIG 14F illustrates the estimate of the number of locally bottlenecked VCs,
• VBR background traffic was generated by a deterministic on/off source with the peak rate and the lengths of on and off periods are, respectively, 10Mbps, 20 ⁇ maxsecs, and
• FIGs 15A to 15F illustrate simulation results in the parking lot configuration with ER marking and VCR background traffic
• FIG FIG 15C illustrate a queue length at the switch SW3
• FIG 15D illustrates a queue length at the switch SW4
• FIG 15D illustrates the estimate of the number of locally bottlenecked VCs,
• FIG 15E illustrates the estimate of the number of locally bottlenecked VCs,
• the transient overshooting of the ABR queue length of the switch SW3 was substantially reduced with its maximum decreasing from 6,000 cells to 3,200 cells Obviously, this gain comes at the cost of temporary oscillation of the queue length and the source transmission rates as observed in FIGs 15 A, 15B, and 15C
• the ER allocation algorithm according to the embodiment of the present invention effectively takes the control back and hence recovers the queue length behavior from the oscillatory mode to the asymptotic mode
• the ER allocation algorithm is advantageous in that (1) maximal link utilization and minimal cell loss are guaranteed regardless of RTDs in an ABR closed loop; (2) ABR queue size requirements are minimized by ensuring asymptotical stabilization of ABR queues (3) the MAX-MIN fairness based on the ATM forum standards is guaranteed by ensuring a fair share of an available bandwidth to each user, (4) communication network environmental change is fast reacted to such as changes in the number of ABR users and the ABR bandwidth, (5) all functions including EFCI, RR, and ER markings are provided as specified in the ATM forum traffic management specification, (6) high utilization, low cell loss, and the MAX-MIN fair rate allocation are achieved through existence of an asymptotically stable operating point, (7) high responsiveness and transient control performance to network loading changes is achieved at multiple time scales, I e , at the cell level rate changes of VBR and ABR VCs and at the cell level arrivals and departures of VBR and ABR VCs,

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