Decision Optimization Techniques for Efficient Delivery of Multimedia Streams Mugurel Ionut Andreica, Nicolae Tapus Politehnica University of Bucharest, Computer Science & Engineering Department

2 Summary Motivation Context Improving Heuristics based on Conflict Graphs Online Analysis of Traffic (Self-) Similarity K th Best Resource Selection Conclusions & Future Work

3 Motivation QoS guarantees for multimedia streams – strictly necessary –minimum required bandwidth –(more or less) constant latency –reduced jitter well-established QoS improvement solution –bandwidth reservation mechanism requires: –new business model from ISPs –lease network links for short(er) durations, but providing guaranteed end-to-end bandwidths –(currently: flat fee lease of constant upload/download bandwidth links; not end-to-end)

4 Context - Data Transfer Scheduling Model (1/2) one (centralized) data transfer manager –knows the network topology (structure) –has full control over the network many data transfer requests –duration (D) (non-preemptive = a contiguous time interval) –earliest start time (ES) –latest finish time (LF) –minimum required bandwidth (B min ) –source (src) –destination (dst) –profit (pr)

5 Context - Data Transfer Scheduling Model (2/2) request handling modes –batch mode (multiple requests at a time) conflicts between the requests in the same batch are modeled by using conflict (hyper-)graphs heuristic algorithms are used in order to (repeatedly) compute maximum weight (profit) independent sets –online mode (1 request at a time) handle the requests in the order of arrival verify if the request can be granted (satisfying the request’s constraints/parameters) grant the request (resource allocation/reservation) or reject it –interpretation of time: time slot-based (discrete) or event- based (continuous) low response times –a complex strategy would take too long –even a simple strategy may take too long! => need some efficient techniques (data structures)

6 Context - Data Transfer Scheduling Framework multiple (interconnected) modules

7 Improving Heuristics based on Conflict Graphs (1/2) pairs of data transfer requests may be in conflict –they require exclusive access to the same network resources, during overlapping time intervals construct a conflict graph CG compute a maximum weight independent set (MWIS) in CG –i.e. select a set of non-conflicting requests with maximum total weight

8 Improving Heuristics based on Conflict Graphs (2/2) computing MWIS : NP-hard heuristics based on repeated vertex extraction –in case of unit weights: as long as CG contains any more edges (conflicts): extract (remove) from CG the vertex with the largest degree algorithm for implementing the above heuristic in O(N+M) time –N=number of vertices in CG –M=number of edges in CG extensions to other types of repeated vertex extraction heuristics (e.g. minimum degree, maximum number of already extracted neighbors, etc.)

9 Online Analysis of Traffic (Self-) Similarity (1/3) 2 arrays tr1 and tr2 of T values (one value per time slot) a function eval(x,y) (e.g. |x-y|) an aggregate function aggf (e.g. +,max) answer efficiently the following types of queries: –Q(a,b,len)=aggf(eval(tr1(a+i), tr2(b+i))) (0≤i≤len-1) self-similarity queries when tr1=tr2 such queries: useful for traffic analysis & traffic pattern detection

10 Online Analysis of Traffic (Self-) Similarity (2/3) we divide the T time slots into T/k groups of k time slots each (the last group may be shorter) group j: time slot interval [left(j),right(j)] –nslots(j)=right(j)-left(j)+1 compute Tagg(i,j)=eval(tr(1)(i+q), tr(2)(left(j)+q)) (0≤q≤nslots(j)-1; 1≤i≤T- nslots(j)+1) => O(T 2 ) preprocessing

11 Online Analysis of Traffic (Self-) Similarity (3/3) Q(a,b,len): can answer in O(1) time for an interval of approx. k slots => O(k+T/k) can also allow updates: change the value of tr1(i) (tr2(i)) to v O(T·k) per update (if aggf is not invertible) O(T) time if aggf has an inverse

12 K th Best Resource Selection each resource (e.g. network path) has d features (e.g. bandwidth, latency, etc.) => modelled as a d-dimensional point –plus a weight (e.g. how valuable it is) select the K th largest weight among all the resources whose d features belong to an orthogonal range –we do not want to always allocate the best resource use a multi-dimensional data structure (for efficient ortogonal range counting queries) + binary search the K th weight

13 Conclusions & Future Work introduced –data transfer scheduling model –data transfer scheduling framework developed techniques for –improving heuristics based on clonflic graphs –online analysis of traffic data –resource selection (and allocation) future work –large-scale testing of the proposed techniques the data transfer scheduling framework is already implemented –develop new algorithms for scheduling multimedia streams

14 Thank You !