Factores de riesgo y de protección de la reincidencia

Caching content locally results in shorter routes to content and hence lower power consumption. This strategy however results in increased equipment power consumption through the deployment of local caches. A trade-off has to be struck therefore where the optimum cache size is a function of the two above drivers. This evaluation aims to minimise the power consumption of a video service by optimising the sizes of caches deployed at the nodes. It takes into account a VoD service deploying an IP over WDM network with the network architecture described in Figure 2-3 in Chapter 2.

4.2.1 Fixed Cache MILP Model

This MILP model finds the optimum cache size to be deployed at each node in the network to minimise power consumption. Caches are considered having a fixed size that is fully operated for the whole day. The model declares a number of sets, parameters and variables as follows:

Sets:

𝑁 Set of nodes

63 𝑁𝑚_𝑖 Set of neighbouring nodes of node i

𝑇 Set of points in time

𝐾 Set of equations that approximate the convex function describing the relationship between the cache and its hit ratio.

Parameters:

𝑃𝑝 Power consumption of a router port

𝑃𝑜_𝑖𝑡 Power consumption of optical switch i at time t

𝑃𝑡 Power consumption of a transponder

𝑃𝑎 Power consumption of an amplifier

𝑃𝑚𝑑 Power consumption of a multiplexer/demultiplexer

𝐵 Capacity of a wavelength

𝑊 Number of wavelengths in a fibre

𝐷_𝑖𝑗 Distance from node i to j

𝑆 Span distance between two amplifiers

𝐴𝑚𝑝_𝑖𝑗 Number of amplifiers used on each fibre on the physical link from node i to j, 𝐴𝑚𝑝_𝑖𝑗 = ⌊𝐷𝑖𝑗/𝑆 − 1⌋ + 2

𝑅𝑃𝑚𝑎𝑥_𝑥 Maximum router ports available to node x

𝜆^𝑥𝑦𝑡 Demand from node x to y at time t

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𝛿_𝑖 Is 1 if node i has a video server, 0 otherwise, ∑_𝑖∈𝑁𝛿_𝑖 = 𝑢, where u is the total number of servers in the network

𝑅𝑢 Server ratio of uplink demand to regular traffic

𝑅𝑑 Server ratio of downlink demand to regular traffic

𝛷 Cache power consumption factor in W/GB

𝑎, 𝑏 Approximation vectors

Variables:

𝑓_𝑖𝑗 Fibres on the physical link from node i to j

𝜆_𝑖𝑗𝑡^𝑥𝑦 Regular traffic from node i to j, part of the virtual link from node x to y at time t

𝜆𝑢_𝑖𝑗𝑡^𝑥𝑦 Uplink traffic from node i to j, part of the virtual link from node x to y at time t

𝜆𝑑_𝑖𝑗𝑡^𝑥𝑦 Downlink traffic from node i to j, part of the virtual link from node x to y at time t

𝑤_𝑖𝑗𝑡^𝑥𝑦 Wavelengths on the link from node i to j, part of the virtual link from node x to y at time t

𝑤_𝑖𝑗𝑡 Wavelengths on the physical link from node i to j at time t

𝐶_𝑥𝑦𝑡 Wavelengths on the virtual link from node x to y at time t

65 𝐴𝑃_𝑖𝑡 Aggregation ports at node i at time t

𝐻 Cache hit ratio

𝑀 Cache size in GB

Under lightpath bypass, the power consumption of the network consists of the power consumption of the following components:

1. Router ports at time t, where a port is required for each occupied wavelength:

∑ 𝑃𝑝 (𝐴𝑃_𝑖𝑡 + ∑ 𝐶_𝑖𝑗𝑡

66 6. Deployed caches at time t:

∑ ∅𝑀

𝑖∈𝑁

It is worth mentioning that the model does not assume a simple symmetric case, and therefore, the number of lightpaths from node i to j can be different to the number of lightpaths in the reverse direction. Mainly, fij , wijt and Cijt are not necessarily equal to fji, wjit and Cjit, respectively. Note that uplink traffic is the video traffic uploaded from nodes to video servers, downlink traffic is the video traffic downloaded from video servers to nodes and regular traffic is other non-cacheable traffic (email, live video, dynamic content, etc.).

The goal of the proposed MILP model is to minimise the network total daily power consumption while satisfying a number of flow and capacity constraints. The complete MILP model is defined as:

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Objective (4-1) calculates the power consumption of the network by summing up the power consumption of different network components at each time point. Constraints (4-2) and (4-3) limit the number of occupied router ports at each node to its maximum.

Constraint (4-4) and (4-5) are the capacity constraints for the optical layer. Constraint (4-6) is the flow conservation constraint in the optical layer. Constraint (4-7) is the flow conservation constraint for regular traffic in the IP layer. Constraints (4-8) and (4-9) differ from Constraint (4-7) by considering the uplink and downlink traffic terminating and originating at nodes equipped with a video server, respectively.

Constraint (4-10) ensures that the total regular, uplink and downlink traffic carried by a lightpath does not exceed its capacity. Constraint (4-11) calculates the number of required aggregation ports. Finally, Constraint (4-12) is the piecewise linear approximation utilised to find the cache size M from its hit ratio H.

4.2.2 Variable Cache MILP Model

The variable cache MILP model finds the optimum cache size of each node varied over the time of the day. The model assumes that caches are equipped with sleep-mode

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capabilities such that inactive parts of a cache can go to sleep. The goal is to explore the potential additional power savings on top of the use of fixed caches and to analyse the variation in optimum cache sizes that minimise power consumption with the variation in network traffic.

The variable cache MILP model defines the same sets, parameters and variables defined for the fixed cache MILP model. Since cache sizes are variable for each node at each time of the day, the cache size variable M and its hit ratio H are modified as

In addition, Constraints (4-9), (4-11) and (4-12) are modified as follows:

∑ 𝜆𝑑_𝑖𝑗𝑡^𝑥𝑦

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𝐴𝑃_𝑖𝑡 = ∑ (𝜆^𝑖𝑦𝑡+ 𝜆^𝑖𝑦𝑡∙ 𝑅𝑢 ∙ 𝛿_𝑦+ 𝜆^𝑦𝑖𝑡∙ 𝑅𝑑 ∙ 𝛿_𝑦∙ (1 − 𝐻_𝑖𝑡 ))

𝑦∈𝑁:𝑦≠𝑖

/𝐵

∀ 𝑖 ∈ 𝑁, ∀ 𝑡 ∈ 𝑇

(4-15)

𝑀_𝑖𝑡 ≥ 𝑎_𝑘∙ 𝐻_𝑖𝑡+ 𝑏_𝑘

∀ 𝑘 ∈ 𝐾 (4-16)

4.3 Constraint-Based Genetic Algorithm and