Lecture 17. ATM VPs, circuit-switching D. Moltchanov, TUT, Spring 2008 D. Moltchanov, TUT, Spring 2015

Outline ATM virtual path design Telephone network: single BH Telephone network: multiple BH

ATM virtual path design

Asynchronous transfer mode (ATM) Concept of virtual paths (VP) and virtual circuits (VC) VP: permanent/semi-permanent connections Several VC multiplexed into one VP Similar to MPLS but completely separate from IP network Still used mainly in US Could be: IP/ATM/SONET or something like this…

ATM virtual path design Problem we consider Analysis is as usual Get demands constraints: how demands are realized over path Get capacity constraints: which flows are using links (link loads) Analyzing the problem We have set of paths for demand d: Unsplittable (non-bifurcated) solution is needed We need a binary variable Tells us whether a path is chosen or not which gives us demand constraint How to determine the link capacity such that the total link cost is minimized given a set of unsplittable demands and modular link units of 155Mbps?

ATM virtual path design Continuing Total number of VPs using link e At most one flow will use link e for each demand due to If a flow uses link then full demand is realized over this link The link load is then Assume that demand volume and link rates are in units of 155Mbps where link rate for link e is an integer

ATM virtual path design Objective function We are to minimize cost Let unit cost of 155Mbps be in link e The whole problem Minimize Subject to where is binary, are integers Integer programming (IP) problem! Complex to solve! Applicable to MPLS directly…

ATM virtual path design: LP vs. IP problem Recall similar problem minimize subject to We have here IP version of LP problem minimize subject to binary integers Note: way more complex to solve compared to LP

Circuit-switched telephony: single BH

Telephony: single busy hour design Nodes in telephony networks End nodes Transit nodes End nodes (access nodes) Digital exchanges generating demand Demand is expressed in Erlangs During the busy hour Network is underloaded at other times Transit nodes: do not generate demands, act as relays The describe the load we need be the average arrival rate be the average duration of a call the offered traffic load is then 1 Erl:

Telephony: circuits/trunks Circuits/trunks Calls require 64Kbps Calls require path for the whole duration of a session Path may traverse se sequence of transit nodes Links between nodes: trunk-groups or circuit-groups Installation of trunks Typically installed in module US/Japan T1 (1.5Mbps) – 24 trunks Rest of the world: E1 (2.048Mbps) – 30 trunks (+2 signaling, 0 and 16) Modular link capacity: a number of E1 trunks, 30,60,90,…! 1 LCU = 30, DVU are arbitrary integers

Telephony: problem and GoS Problem we are to solve What is grade-of-service (GoS)? Set of metrics attributed to traffic performance in the network Simply: allowed call dropping probability (CDP) Dropping: all resources are busy Telephone networks GoS is different for different type of calls Local: 5-8% CDP during BH International: 1-3% during BH Cellular? 5-8% during BH Networks are always designed for BH! How to determine the modular capacity needed in the network so that the offered traffic is carried with some acceptable grade of service (GoS)?

Telephony: call routing Call routing According to fixed rules Using a set of predefined routes Example demand d: end nodes 1 and 2 there are three available routes, P d =3 (1,3,7,6,2), (1,3,7,6,4,2) uses end-node 7 which is not allowed route (1,2,6,4,2) just prohibited Possible routing rule Split demand between routes such that and we are getting demand constraints Implemented using load sharing: route p with probability

Telephony: call routing Links load (taking into account load sharing) are where is 1 if link e belongs to path p of demand d Important notes link load: average offered traffic to link e (Erl.) average number of calls in progress given no losses on a link! given that the link has infinite capacity! Let be the call blocking probability for link e, i.e. a is the offered load c is the number of trunks (circuits) probability that all servers are busy in M/M/c/c queue

Telephony: call routing However, we want to get c for a certain (a,b) Forward formula gives b for certain (a,c) Let c=C(a,b) be inverse of Erlang-B loss formula Function C(a,b) is concave in a for any b

Telephony: call routing Link dependent dimensioning function where is a certain dimensioning constant (e.g. 1% of losses) gives real number of circuits to carry offered load a The whole problem For offered demands, blocking and unit modular capacity cost Minimize Subject to where continuous non-negative, integers Concave-integer dimensioning problem

Circuit-switched telephony: multiple BHs

Telephony: multiple BHs We considered the case Busy hours of all demands coincide E.g. all happen at, say 15:00-16:00 May only happen in local proximity Same time-zone, small country inside a single time-zone US as an example 8:00 AM Eastern time zone (NY, Boston, Washington) 5:00 AM Pacific time zone (LA, San-Francisco, Seattle) BHs do not coincide due to time difference Beneficial for large carriers Decrease the capacity needed Route via “still” or “already” lightly loaded regions Why call prices are that high? Network is unloaded anyway!

Telephony: routing of calls again Routing in Fixed-order of routes + load sharing Routing 1980 onwards Dynamic non-heirarchial routing (DBHR) Dynamically controlled routing (DCR) Dynamic alternative routing (DAR) Real-timer network routing (RTNR) Common: free capacity due to non-coincidence of BHs One time zone is used as a reference Applied to core network, e.g. transit nodes

Telephony: routing of calls again Problem we consider New demand representation Partition a day into several “traffic hours” t=1,2,…,T For each demand its traffic is different at different intervals Set of demand volume vectors Paths is real networks May contain at most two links In other words may traverse at most one intermediate hop We do not even need an algorithm to get them… How to do modular capacity design given that traffic volume is different for different times of a day and by taking into account functional characteristics of a routing scheme.

Telephony: routing of calls again Dynamic nature of a flow Routing should be different at different traffic hours, t=1,2,…,T Demand d for path p at time t is denoted as The whole problem For demands, blocking, modular capacity cost and t=1,2,…,T Minimize Subject to where are non-negative continuous, are integers Similar concave-integer programming problem

Telephony: routing of calls again Nodes on dynamic routing Add another dimension of flexibility Solution is only slightly more complex can be made time-dependent Slightly higher blocking during the links’ busy period Multi-BH scenario for packet-switching Dynamic routing is good for packet networks Dependence of time zones is also evident Similar to voice traffic Different traffic matrices for different time of a day May result in substantial cost savings Adds implementation complexity