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On Processor Sharing (PS) and Its Applications to Cellular Data Network Provisioning. Yujing Wu, Carey Williamson , Jingxiang Luo Department of Computer Science University of Calgary. Motivation.

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on processor sharing ps and its applications to cellular data network provisioning

On Processor Sharing (PS) and Its Applications to Cellular Data Network Provisioning

Yujing Wu, Carey Williamson, Jingxiang Luo

Department of Computer Science

University of Calgary

IFIP Performance 2007

motivation
Motivation
  • Insensitivity of network performance to the traffic details is a desirable property, since it facilitates robust traffic engineering.
  • Example: Erlang B call blocking formula
  • How about 3G cellular data networks? Are performance measures sensitive to the detailed traffic characteristics (e.g., flow size distribution, flow inter-arrival time, number of flows, correlations) or not?

IFIP Performance 2007

synopsis of paper
Synopsis of Paper
  • Q: Processor Sharing (PS) = insensitivity?
    • Egalitarian Processor Sharing (EPS): yes
    • Discriminatory Processor Sharing (DPS): no
  • DPS is a better model of cellular networks with Proportional Fairness (PF) scheduling
  • Insensitivity study carried out for DPS
    • DPS is “approximately insensitive”
    • EV-DO simulation study verifies DPS results
  • Results do not hold for differentiated services

IFIP Performance 2007

key contributions
Key Contributions
  • Improve the understanding of PS
    • Prove the strict insensitivity of EPS in a relevant new case (i.e., finite capacity EPS)
    • Systematically investigate the approximate insensitivity of DPS by simulation
  • Apply these findings to traffic engineering for the downlink in 3G cellular data networks
    • Practical insensitivity when PF scheduling is used
    • Sensitivity when supporting differentiated services

IFIP Performance 2007

outline
Outline
  • Motivation & Contributions
  • Modeling cellular data networks
  • EPS and DPS results
  • Simulation of a cellular system
  • Service differentiation
  • Summary

IFIP Performance 2007

downlink model for a cellular data network

current feasible rate: r( i )

PF

scheduler

data

flow 1

CAC

forward link

data

flow 2

MS

...

...

C(t)

data

flow n

TDM

1.667ms

frame

MS

MS

Downlink Model for a Cellular Data Network

flow arrivals

schedule flow i at slot t

feasible rate of flow j at slot t

propagation loss, shadowing, fast fading

realized throughput of flow j up to slot t

IFIP Performance 2007

modeling cellular networks
Modeling Cellular Networks
  • The downlink of the cellular system behaves like a PS queue with respect to the flow-level performance
  • With different assumptions about rate variations, the system can be abstracted to different models.
    • Homogenous rate variation (idealized situation): the feasible rate fluctuates around the mean for all active flows, and these fluctuations are statistically identical for all users.
    • Heterogeneous rate variation: the feasible rate fluctuations around the mean for active flows are statistically different. PF allocates more time to users with lower variability in the feasible rate.

EPS

DPS

IFIP Performance 2007

traffic model i poisson flow arrivals
Traffic model I: Poisson flow arrivals

Poisson process

The flow size distribution is general.

IFIP Performance 2007

traffic model ii poisson session arrivals
Traffic model II: Poisson session arrivals

session arrival epochs (Poisson process)

  • distribution of number of flows per session
  • flow size distribution
  • think time distribution
  • correlation in successive flow and think time statistics

general session structure

Flows in a session

flexibility to model more realistic traffic.

IFIP Performance 2007

outline1
Outline
  • Motivation & Contributions
  • Modeling cellular data networks
  • EPS and DPS results
  • Simulation of a cellular system
  • Service differentiation
  • Summary

IFIP Performance 2007

eps queue results
EPS Queue Results
  • Insensitivity has been proven for:
    • Poisson flow arrivals without blocking [Cohen; Kelly]
    • Poisson session traffic with infinite capacity [Bonald et al. 2001abc; Bonald 2006; Borst 2003]
  • We prove that the joint queue length distribution, mean number of active flows, and blocking probabilities are insensitive to the session structure in the finite-capacity EPS queue fed by Poisson session arrivals.

IFIP Performance 2007

finite capacity eps system
Finite Capacity EPS system
  • Model the system by a queueing network with a restricted state space.
  • Apply results from stochastic queueing network theory for the proof. (see paper)
  • Value? Assuming homogenous rate variation in the cellular system, we can replace the complicated Poisson session traffic with simple Poisson flows with exponentially distributed flow sizes. The simplified model will suffice for provisioning purposes.

IFIP Performance 2007

dps queue results
DPS Queue Results
  • Rigorously speaking, performance is sensitive to the traffic details [Bonald 2004]
  • Insensitive bounds and limiting approximations exist. [Fayolle 1980; van Kessel 2005; Bonald 2004; Boxma 2006]
  • Do the insensitivity properties of EPS systems approximatelycarry over to DPS for certain parameter choices?

IFIP Performance 2007

dps model of 3g system
DPS Model of 3G System
  • M flow types
  • Within type m, lm subclasses reflecting unequal sharing of time slots
  • Assume all flows are geographically placed uniformly at random in the cell site, independent of their types.

IFIP Performance 2007

dps simulation model
DPS Simulation Model
  • Single class of traffic, but different flow weights
  • Finite-capacity: at most 15 concurrent flows
  • Two types of Poisson session traffic
    • Type 1: 5 flows/session (deterministic) , LN flow size (mean 2, CV 3), HyperExp thinking time (mean 1, CV 3)
    • Type 2: Geo dist. for flow/session (mean 10), exp dist. thinking time (mean 0.05), flow sizes being one of five dist. (Deterministic, Exp, HyperExp, LN, Pareto)
  • Change session details of type 2 and compare the results to those in the case where both types are Poisson flows with exponentially distributed sizes.

IFIP Performance 2007

dps simulation results
DPS Simulation Results

Wi=[1, 2], i=1, 2

Wi=[1, 10], i=1, 2

IFIP Performance 2007

dps observations
DPS Observations
  • Flow details (session structure) have little impact on the first-order system performance unless the weights among different flows are highly skewed (e.g., the weight ratio is 10 or more).
  • In practical cellular systems, the unequal slot sharing among flows caused by PF scheduling and by heterogeneous rate variations is only modest (e.g., weight ratio is less than 2).
  • It is conjectured that traffic details do not affect the metrics relevant to network provisioning.

IFIP Performance 2007

outline2
Outline
  • Motivation & Contributions
  • Modeling cellular data networks
  • EPS and DPS results
  • Simulation of a cellular system
  • Service differentiation
  • Summary

IFIP Performance 2007

ev do system model
EV-DO System Model
  • Simulate a shared downlink data channel of the central cell site surrounded by interfering cells (6 direct neighbours, and 12 outer cells).
  • All BSs transmit at full power on the downlink.
  • The channel model includes propagation loss, slow fading, and fast fading.
  • Flows are placed uniformly at random in the center cell, and users do not move during flow transmission. Each active flow has a time-varying SINR updated at every slot.

IFIP Performance 2007

static user scenario

node 1

node 6

x

x

x

x

x

x

Static User Scenario

PF unfairness exists, but it is not extreme!

BS

IFIP Performance 2007

dynamic user scenario
Dynamic User Scenario

No blocking

Poisson flow arrivals

flow size: m=50kB

Poisson session arrivals

flows per session: geometric dist., m=30;

think time: exp dist., m=5s

flow size: m=50KB

Approximate insensitivity!

IFIP Performance 2007

outline3
Outline
  • Motivation & Contributions
  • Modeling cellular data networks
  • EPS and DPS results
  • Simulation of a cellular system
  • Service differentiation
  • Summary

IFIP Performance 2007

service differentiation
Service Differentiation
  • Deliberately treat traffic unequally at the type level (i.e., strict priority)
  • To what extent does the weight asymmetry among traffic types change the insensitivity property?
  • A DPS system with two types of Poisson flow arrivals, each with a single subclass.

IFIP Performance 2007

dps with differentiated service
DPS with Differentiated Service

Change flow size distribution of high priority traffic type

Change flow size distribution of low priority traffic type

IFIP Performance 2007

service differentiation results
Service Differentiation Results
  • Compared to the bias among subclasses, the bias among traffic types manifests sensitivity in a much more dramatic way.
  • Depending on the traffic priority, variability in the flow size distribution has different impacts.
  • Using simple traffic models may lead to under-estimation or over-estimation of performance in the cellular system when differentiated services are deployed.

IFIP Performance 2007

summary
Summary
  • Studied EPS/DPS models of cellular networks
  • Extended the theoretical analysis of the EPS insensitivity to a new finite-capacity case.
  • Showed that the first-order performance of DPS systems is approximately insensitive to the session structure in relevant regime for practical parameter settings.
  • Simple and robust traffic engineering is possible for cellular systems using DPS for PF scheduling.
  • The introduction of differentiated services may pose a great challenge for future cellular network provisioning.

IFIP Performance 2007