Max-min fairness
Encyclopedia
In communication networks and multiplexing
, a division of the bandwidth resources is said to be max-min fair when: firstly, the minimum data rate that a dataflow achieves is maximized; secondly, the second lowest data rate that a dataflow achieves is maximized, etc.
In best-effort statistical multiplexing
, a first-come first-served (FCFS) scheduling policy is often used. The advantage with max-min fairness over FCFS is that it results in traffic shaping
, meaning that an ill-behaved flow, consisting of large data packets or bursts of many packets, will only punish itself and not other flows. Network congestion
is consequently to some extent avoided.
Fair queuing is an example of a max-min fair packet scheduling algorithm for statistical multiplexing
and best effort packet-switched networks, since it gives scheduling priority to users that have achieved lowest data rate since they became active. In case of equally sized data packets, round-robin scheduling
is max-min fair.
s) provide high average throughput but low stability in the service quality, meaning that the achieved service quality is varying in time depending on the behavior of other users. If this instability is severe, it may result in unhappy users that will choose another more stable communication service.
Max-min fair resource sharing results in higher average throughput (or system spectral efficiency in wireless networks) and better utilization of the resources than a work-conserving equal sharing policy of the resources. In equal sharing, some dataflows may not be able to utilize their "fair share" of the resources. A policy for equal sharing would prevent a dataflow from obtaining more resources than any other flow, and from utilizing free resources in the network.
On the other hand, max-min fairness provides lower average throughput than maximum throughput resource management, where the least expensive flows are assigned all capacity they can use, and no capacity might remain for the most expensive flows. In a wireless network, an expensive user is typically a mobile station at far distance from the base station, exposed to high signal attenuation. However, a maximum throughput policy would result in starvation
of expensive flows, and may result in fewer "happy customers".
A compromise between max-min fairness and maximum throughput scheduling is proportional fairness, where the resources are divided with the goal to achieve the same cost to each user, or to minimize the maximum cost per unit that a dataflow reaches. Expensive data flows achieves lower service quality than others in proportional fairness, but does not suffer from starvation. Max-min fairness results in more stable service quality, and therefore perhaps "happier customers".
Consider i data flows, sometimes called users or sources. Each data flow has a defined initial node, a destination node, and a desired data rate. A flow on its path through the network may be divided between "parallel" links, in a load balancing
scheme.
An allocation vector x whose i-th coordinate is the allocation for flow i, i.e. the rate at which the user i is allowed to emit data.
An allocation of rates x is “max-min fair” if and only if an increase of any rate within the domain of feasible allocations must be at the cost of a decrease of some already smaller rate.
Depending on the problem, a max-min fair allocation may or may not exist. However, if it exists, it is unique.
The name “max-min” comes from the idea that it is the rate of the smaller (or minimum) flows that is made as large as possible (maximized) by the algorithm. Hence we give higher relative priority to small flows. Only when a flow asks to consume more than C/N (link capacity/number of flows) is it at any risk of having its bandwidth throttled by the algorithm.
A data rate allocation is max-min fair if and only if a data flow between any two nodes has at least one bottleneck link.
Multiplexing
The multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...
, a division of the bandwidth resources is said to be max-min fair when: firstly, the minimum data rate that a dataflow achieves is maximized; secondly, the second lowest data rate that a dataflow achieves is maximized, etc.
In best-effort statistical multiplexing
Statistical multiplexing
Statistical multiplexing is a type of communication link sharing, very similar to dynamic bandwidth allocation . In statistical multiplexing, a communication channel is divided into an arbitrary number of variable bit-rate digital channels or data streams. The link sharing is adapted to the...
, a first-come first-served (FCFS) scheduling policy is often used. The advantage with max-min fairness over FCFS is that it results in traffic shaping
Traffic shaping
Traffic shaping is the control of computer network traffic in order to optimize or guarantee performance, improve latency, and/or increase usable bandwidth for some kinds of packets by delaying other kinds of packets that meet certain criteria...
, meaning that an ill-behaved flow, consisting of large data packets or bursts of many packets, will only punish itself and not other flows. Network congestion
Network congestion
In data networking and queueing theory, network congestion occurs when a link or node is carrying so much data that its quality of service deteriorates. Typical effects include queueing delay, packet loss or the blocking of new connections...
is consequently to some extent avoided.
Fair queuing is an example of a max-min fair packet scheduling algorithm for statistical multiplexing
Statistical multiplexing
Statistical multiplexing is a type of communication link sharing, very similar to dynamic bandwidth allocation . In statistical multiplexing, a communication channel is divided into an arbitrary number of variable bit-rate digital channels or data streams. The link sharing is adapted to the...
and best effort packet-switched networks, since it gives scheduling priority to users that have achieved lowest data rate since they became active. In case of equally sized data packets, round-robin scheduling
Round-robin scheduling
Round-robin is one of the simplest scheduling algorithms for processes in an operating system. As the term is generally used, time slices are assigned to each process in equal portions and in circular order, handling all processes without priority . Round-robin scheduling is simple, easy to...
is max-min fair.
Comparison with other policies for resource sharing
Generally, policies for sharing resources that are characterized by low level of fairness (see fairness measureFairness measure
Fairness measures or metrics are used in network engineering to determine whether users or applications are receiving a fair share of system resources. There are several mathematical and conceptual definitions of fairness.-TCP fairness:...
s) provide high average throughput but low stability in the service quality, meaning that the achieved service quality is varying in time depending on the behavior of other users. If this instability is severe, it may result in unhappy users that will choose another more stable communication service.
Max-min fair resource sharing results in higher average throughput (or system spectral efficiency in wireless networks) and better utilization of the resources than a work-conserving equal sharing policy of the resources. In equal sharing, some dataflows may not be able to utilize their "fair share" of the resources. A policy for equal sharing would prevent a dataflow from obtaining more resources than any other flow, and from utilizing free resources in the network.
On the other hand, max-min fairness provides lower average throughput than maximum throughput resource management, where the least expensive flows are assigned all capacity they can use, and no capacity might remain for the most expensive flows. In a wireless network, an expensive user is typically a mobile station at far distance from the base station, exposed to high signal attenuation. However, a maximum throughput policy would result in starvation
Resource starvation
In computer science, starvation is a multitasking-related problem, where a process is perpetually denied necessary resources. Without those resources, the program can never finish its task....
of expensive flows, and may result in fewer "happy customers".
A compromise between max-min fairness and maximum throughput scheduling is proportional fairness, where the resources are divided with the goal to achieve the same cost to each user, or to minimize the maximum cost per unit that a dataflow reaches. Expensive data flows achieves lower service quality than others in proportional fairness, but does not suffer from starvation. Max-min fairness results in more stable service quality, and therefore perhaps "happier customers".
Max-min fair link capacity pre-allocation
Max-min fairness in communication networks assumes that resources (capacities of communication links) are allocated to flows in advance, as opposed to best-effort networks.Consider i data flows, sometimes called users or sources. Each data flow has a defined initial node, a destination node, and a desired data rate. A flow on its path through the network may be divided between "parallel" links, in a load balancing
Load balancing (computing)
Load balancing is a computer networking methodology to distribute workload across multiple computers or a computer cluster, network links, central processing units, disk drives, or other resources, to achieve optimal resource utilization, maximize throughput, minimize response time, and avoid...
scheme.
An allocation vector x whose i-th coordinate is the allocation for flow i, i.e. the rate at which the user i is allowed to emit data.
An allocation of rates x is “max-min fair” if and only if an increase of any rate within the domain of feasible allocations must be at the cost of a decrease of some already smaller rate.
Depending on the problem, a max-min fair allocation may or may not exist. However, if it exists, it is unique.
The name “max-min” comes from the idea that it is the rate of the smaller (or minimum) flows that is made as large as possible (maximized) by the algorithm. Hence we give higher relative priority to small flows. Only when a flow asks to consume more than C/N (link capacity/number of flows) is it at any risk of having its bandwidth throttled by the algorithm.
Bottleneck links
A bottleneck link for a data flow i is a link that is fully utilized (is saturated) and of all the flows sharing this link, the data flow i achieves overall maximum data rate. Note that this definition is substantially different from a common meaning of a bottleneck. Also note, that this definition does not forbid a single bottleneck link to be shared between multiple flows.A data rate allocation is max-min fair if and only if a data flow between any two nodes has at least one bottleneck link.
Progressive filling algorithm
If resources are allocated in advance in the network nodes, max-min fairness can be obtained by using an algorithm of progressive filling. You start with all rates equal to 0 and grow all rates together at the same pace, until one or several link capacity limits are hit. The rates for the sources that use these links are not increased any more, and you continue increasing the rates for other sources. All the sources that are stopped have a bottleneck link. This is because they use a saturated link, and all other sources using the saturated link are stopped at the same time, or were stopped before, thus have a smaller or equal rate. The algorithm continues until it is not possible to increase. Lastly, when the algorithm terminates, all sources have been stopped at some time and thus have a bottleneck link. This allocation is max-min fair.See also
- Fairness measureFairness measureFairness measures or metrics are used in network engineering to determine whether users or applications are receiving a fair share of system resources. There are several mathematical and conceptual definitions of fairness.-TCP fairness:...
s - SchedulingScheduling (computing)In computer science, a scheduling is the method by which threads, processes or data flows are given access to system resources . This is usually done to load balance a system effectively or achieve a target quality of service...
in multitasking operational systems.