# Scalable service migration in autonomic network environments

## Summary (2 min read)

### Introduction

- The problem of determining the optimal location of a service facility is revisited and addressed ina way that is both scalable and deals inherently with network dynamicity.
- For such environments, a new policy (referred to 2 as Migration Policy E) is proposed that moves the facility until the end of a monotonically cost decreasing path, provided that tentative movements to the one-hop neighbor nodes are allowed.
- In order to deal with the increased complexity, several near-optimal approaches have been proposed that can be categorized as either centralized or distributed [6].
- Let T xt be the shortest path tree in Tt(x) over which data corresponding to the nodes’ service demands are forwarded towards the facility nodex.

### A. Service Migration for a Single Facility

- Consider the case of one facility located at nodex at timet.
- Note that in general shortest path trees are different for different roots (i.e., T yt+1 6= T x t ), except for the special case of topologies with unique shortest path trees [40].
- The following lemmas are the basis for the migration policy presented later.
- In view of Lemma 1, two interesting observations can be made regarding the difference when the facility is located at neighbor nodes.
- Second, it depends on the difference between the aggregate service demands.

### B. Multiple Facilities

- The following theorem shows that under Migration Policy S, overall cost reduction is always achieved (i.e.,Ct+1 < Ct), whatever the number of facilities in the network.
- In a network consisting of a unique shortest path tree, a single service facility always arrives at the optimal location under Migration PolicyS, assuming a static environment, also known as Theorem 3.
- The results of Theorem 3 apply to many real cases.
- Migration PolicyS is also useful for environments that do not comply with the previous conditions, since it allows for cost reduction (even though not necessarily for cost minimization) based on strictly local information.
- In that example, nodes3 and 5 have chosen a shortcut to implement the new shortest path towards the (new) facility node (node3 is a neighbor of the new facility node and node 5 utilizes the path through node3, instead of the one through node6).

### A. Cost Reduction and Tentative Facility Movements

- On the other hand,Λ ( Ix(T yt+1) ) , which is available at node y at time t + 1, could be made available after a tentative facility movement to nodey and then moving back to the previous facility nodex before deciding if a facility movementx t+2 −−→ y should take place.
- Eventually, the condition of Lemma 2 requires information that is not locally available.

### B. Service Migration in Topologies of Equal Link Weights

- The objective is not to determineΦ x t−→y or ( d(v, y) − d(v, x) ) , which are based on non-local information, but rather to exploit the aforementio ed tentative facility movements in such a way that the right term of Lemma 2 becomes obsolete (i.e.,0).
- This is possible in topologies with equal link weights (normalized to1 here), as shown analytically next.
- The following lemma exploits tentative facility movements to allow for further simplification.
- The previous inequality is based on aggregate service demands information that is locally avail ble at the candidate new facility nodey after a tentative facility movement to nodey from the current facility nodex (i.e., Λ ( Ix(T yt+1) ) ) and locally available at nodex after the tentative facility movement back to nodex (i.e., Λ ( Iy(T xt+2) ) ).

### C. Hybrid Policy

- As the tentative movements associated with Migration Policy E introduce overhead (two facility movements per neighbor node), a hybrid policy is proposed here that combines Migration Policy S and E so that tentative movements are avoided whenever possible.
- It is interesting to see that under Migration Policy H , the facility moves to the optimal position in less time (a20 = 1) than under Migration PolicyE (a30 = 1).
- By comparing the results depicted in Figure 5.a and Figure 5.b, it is also interesting to observe that for two facilities: (a) for geometric random graphs,at slightly increases; (b) for Erdős-Rényi random graphs,at remains about the same; and (c) for Albert-Barabási random graphs,at decreases.
- “An improved approximation algorithm for the metric uncapacitated facility location problem,” In W.J. Cook andA.S. Schulz, editors, Integer Programming and Combinatorial Optimization, Volume 2337 of Lecture Notes in Computer Science, pages 240-257, Springer, Berlin, 2002. [14].

### D. Proof of Theorem 3

- The cost corresponding to the facility located at some node v and the facility located at the optimal position (e.g., nodeu), can be shown as monotonically increasing by the number of hops away from the optimal position in a topology of a unique shortest path tree, [3].
- This is due to the fact that the aggregate service demands – corresponding to the particular neighbor (of the facility) node that is towards the optimal position – monotonically increase.
- Since there is a unique shortest path tree, the facility will always move to nodes of lower overall cost (Theorem 1).

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##### Citations

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### Cites background from "Scalable service migration in auton..."

...A slightly different instance of the service migration through locally-determined hops appears in [21]....

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...Centralized approaches assume the existence of some super node that undertakes network-resources management tasks by gathering all required information and bearing the exclusive computation burden of the 1(k)-median problem solution [7]....

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##### References

18,415 citations

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7,736 citations

### "Scalable service migration in auton..." refers methods in this paper

...A simulation tool was written in programming language C for creating network topologies (trees, grids, geometric random graphs [41], Erdős-Rényi random graphs [42], and Albert-Barabási graphs [43]) and implementing the migrat ion policies....

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...In the seque l, migration is studied considering morealistic topologieslike geometric random graphs (suitable for studying mobile ad hoc networks [41]), Erdős-Rényi random graphs (suitable for comparison reasons [42]), and Albert-Barabási graphs (po werlaw graphs that model many modern networks including the Internet [43]), in dynamically changing environments....

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6,991 citations

### "Scalable service migration in auton..." refers background in this paper

...Between a given facility node and any other node in the network, a shortest path route is assumed to be established b y the underlying employed routing protocol, [40]....

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..., T y t+1 6= T x t ), except for the special case of topologies with unique shortest path trees [40]....

[...]

2,271 citations

### "Scalable service migration in auton..." refers methods in this paper

...A simulation tool was written in programming language C for creating network topologies (trees, grids, geometric random graphs [41], Erdős-Rényi random graphs [42], and Albert-Barabási graphs [43]) and implementing the migrat ion policies....

[...]

...In the seque l, migration is studied considering morealistic topologieslike geometric random graphs (suitable for studying mobile ad hoc networks [41]), Erdős-Rényi random graphs (suitable for comparison reasons [42]), and Albert-Barabási graphs (po werlaw graphs that model many modern networks including the Internet [43]), in dynamically changing environments....

[...]

1,333 citations

### "Scalable service migration in auton..." refers background in this paper

..., thek-median problem) is anNP -hard problem for general graphs [2]....

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...The problem of determining the optimal service placement has been studied in the past in areas such as transportation and supply networks [1], and has been approached through the formulation and solution of large optimization problem s (NP -hard) requiringglobal knowledge , as for instance is the case with thek-median problem [2]....

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