Allocated Cell Rate (ACR) Retention

• Source with negotiated ACR but it isn't using it.
  • Why ??
    • Source traffic is inherently bursty.
    • Source is the bottleneck.
• Network is afraid that source(s) will suddenly use the full ACR.
• Network wants a policy to reduce unused ACR's.
  • Such policies are called UILI's (Use it or Lose it).
• On the other hand, source(s) do not like UILI's
  • Why not ??
    • Defeats the purpose of available bit rate (ABR) from source's point of view.
    • ABR is designed to handle bursty traffic.

An even deeper concern… . . . ACR Promotion

Here an uncooperative source could open a connection, but send no data while repeatedly asking for a higher ACR. Once a high enough ACR is grant, the source starts dumping its data at this high rate.

• These issues are still under debate in the ATM Forum.

New Questions: We have assumed that if a switch is congested, it will have some means of computing an appropriate value for the Explicit Rate (ER) of each VCC passing through it.

• But how do we compute good values of Explicit Rate (ER) in switches?
• What would we even mean by "good"?

Max - Min Fairness

Consider a link l and let C_l = link l's capacity.

Consider all ABR VCC's that happen to be using link l

Let ACR_vcc= the allocated rate of such a VCC.
Let F_l= the sum of all VCC's using l.
Assume F_l <= C_l.

ACR_vcc1 > ACR_vcc2

i.e.VCC1 getting more bandwidth than VCC2.

• ACR_vcc2 = PCR_vcc2 (VCC2 is already at its peak rate.)
• There is another link l' (l prime) used by VCC2 with two conditions satisfied:
  • F_l' = C_l'
  • ACR_vcc2 >= ACR_vcc for all other VCC's using l'

Example:

We can maximize network wide throughput at 3 units with

• ACR1 = 0
• ACR_i = 1 where i = 2,3,4.

How do we define fairness? First we need:

An allocation to a set of VCC's is feasible if two conditions are satisfied:

• 0 <= ACR_vcc <= PCR_vcc for all VCC's.
• F_l <= C_l for all links l.

A feasible allocation is max-min fair if for any VCC, raising the ACR_vcc would

1. Make the allocation infeasible, or
2. Force us to decrease another VCC' which already has ACR_vcc'< ACR_vcc.

It is called max-min fairness because it maximizes the user with the smallest allocation, then maximizes the user with the next smallest allocation, and so on.

Example revisited…:

In this case, the max-min allocation is the one which sets ACR = 0.5 for each VCC (see diagram).

Note: Network-wide throughput = 2 (4 VCC * 0.5 each).

Each link has 0.5 + 0.5 and 100% utilization is achieved.

Suppose Instead…

That the capacity on the link from A to B is 2. We still have ACR1 = ACR3 = ACR4 = 0.5, but we can now have ACR2 (A to B) = 1.5.

How to find a max-min fair allocation?

For a feasible allocation, a link l is called a "bottleneck" link for a given VCC if:

• F_l = C_l
• ACR_vcc >= ACR_vcc' for all other VCC' using l

New Example:

The links from B to C and from C to D are "bottleneck" links for VCC3 and VCC4, respectively. Both links are "bottleneck" links for VCC1.

FACT:

A feasible allocation is Max - Min fair, if and only if, each VCC has a "bottleneck" link for this allocation.

"Floating" Algorithm for Computing Max-Min Fair Allocation

Step 0: Initialize ACR to 0 (for all VCC's) and let V = {all VCC's}

Step 1:Raise all ACR's for VCC in V continuously and equally until F_l = C_l on some link l

Step 2: V becomes V - {all VCC's passing through l}

Step 3: If V does not equal the empty set, then go to step 1, else done.

Example Using Floating Algorithm:

Notes taken by Russ Ford from a lecture by Professor Kenneth Vastola @ RPI on 4/21/97.