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Economics of WiFi Offloading: Trading Delay for Cellular Capacity

Joohyun Lee, Yung Yi, Song Chong, Youngmi Jin

arXiv:1207.6607v2cs.NIcs.GT

TL;DR

Cellular traffic growth creates a need to understand whether delayed WiFi offloading can generate incentives for both users and providers. The paper studies this question with a two-stage monopoly market game spanning heterogeneous users, pricing schemes, and delay tolerances, and reports substantial gains in provider revenue and user surplus.

  • Problem

    Users may resist delaying traffic without discounts, while providers may resist offloading because it can reduce chargeable cellular traffic.

  • Method

    The paper models a monopoly provider and price-taking users in a two-stage sequential game with heterogeneous traffic demand, willingness to pay, and multiple pricing schemes.

  • Results

    21% to 152% higher provider revenue and 73% to 319% higher user surplus are reported for delayed WiFi offloading across pricing schemes and delay tolerances.

  • Takeaways & Limitations

    Delayed WiFi offloading is economically beneficial for both providers and users, with revenue in volume pricing exceeding revenue in flat pricing.

Abstract

from arXiv · show

Cellular networks are facing severe traffic overloads due to the proliferation of smart handheld devices and traffic-hungry applications. A cost-effective and practical solution is to offload cellular data through WiFi. Recent theoretical and experimental studies show that a scheme, referred to as delayed WiFi offloading, can significantly save the cellular capacity by delaying users' data and exploiting mobility and thus increasing chance of meeting WiFi APs (Access Points). Despite a huge potential of WiFi offloading in alleviating mobile data explosion, its success largely depends on the economic incentives provided to users and operators to deploy and use delayed offloading. In this paper, we study how much economic benefits can be generated due to delayed WiFi offloading, by modeling a market based on a two-stage sequential game between a monopoly provider and users. We also provide extensive numerical results computed using a set of parameters from the real traces and Cisco's projection of traffic statistics in year 2015. In both analytical and numerical results, we model a variety of practical scenarios and control knobs in terms of traffic demand and willingness to pay of users, spatio-temporal dependence of pricing and traffic, and diverse pricing and delay tolerance. We demonstrate that delayed WiFi offloading has considerable economic benefits, where the increase ranges from 21% to 152% in the provider's revenue, and from 73% to 319% in the users' surplus, compared to on-the-spot WiFi offloading.

I. INTRODUCTION

Delayed WiFi offloading addresses cellular traffic growth by letting delay-tolerant data use future WiFi contacts, but adoption depends on economic incentives for users and providers. The paper models these incentives through a sequential market game and finds substantial gains across pricing and delay settings.

  • Motivation: 18-fold growth in global mobile data traffic was forecast between 2011 and 2016, motivating alternatives to cellular capacity expansion.Cisco projected that the average smartphone would generate 1.3 GB per month in 2015.
  • Delayed WiFi offloading: 60–80% of cellular traffic can be offloaded through delayed WiFi when users tolerate 30 minutes to 1 hour of delay for human mobility.The mechanism exploits users’ mobility to increase the chance of meeting a WiFi AP before a deadline.
  • Economic problem: Delayed offloading requires incentives because users may resist delay while providers may lose chargeable cellular traffic.The paper therefore evaluates economic gains from the perspectives of users, providers, and regulators.
  • Market model: The paper models a monopoly provider and price-taking users in a two-stage sequential game with flat, volume, two-tier, and congestion pricing.Users differ in traffic demand and willingness to pay, while the analysis also varies delay tolerance and traffic conditions.
  • Pricing comparisons: Revenue increases faster under flat pricing than volume pricing, while higher-granularity pricing raises revenue but yields smaller gains as offloading efficiency increases.The paper also reports that delayed offloading’s revenue gain is similar to that from upgrading from 3G to 4G.

2) Traffic model:

The model represents users’ traffic, preferences, mobility-dependent 3G usage, and delay tolerance, then formulates user and provider decisions as utility and revenue maximization problems.

  • User traffic and preferences: Users’ daily demand is temporally split into slot-level traffic, with temporal preference defined by each slot’s share of total demand.Traffic volume cannot exceed demand at each slot, while transmitted traffic may use either 3G or WiFi.
  • Traffic accounting: The model distinguishes total transmitted traffic from charged 3G traffic, whose volume depends on users’ traffic, mobility, and delay profiles.The 3G vector records traffic transferred through cellular service, while the combined vector includes both 3G and WiFi.
  • Delay tolerance: A delay profile specifies the portion of traffic allowed each deadline; traffic not delivered through WiFi by its deadline is transferred immediately through 3G.When no delay is allowed, the model calls the regime on-the-spot offloading.
  • User decision: Users choose transmitted traffic to maximize net utility and subscribe only when that utility is positive.Utility uses an iso-elastic function with increasing but decreasing-marginal-payoff traffic value.
  • Provider decision: The provider selects pricing parameters to maximize expected revenue, defined as income minus network cost, subject to positive revenue and cellular-capacity feasibility.Network cost is modeled as linearly increasing in total 3G traffic.
  • Market structure: The market is modeled as a sequential interaction in which the provider announces prices and users respond with traffic choices.The model includes flat, two-tier, volume, and congestion pricing schemes.

2) Pricing:

The paper compares four pricing schemes and defines traffic, feasibility, and saturation concepts for evaluating how pricing and delay affect offloading and economic outcomes.

  • Pricing schemes: The four pricing schemes are flat, two-tier, volume, and congestion pricing, with parameters controlling fees, usage prices, or time-and-location variation.Flat and two-tier plans can affect subscription, while volume and congestion plans primarily affect traffic volume.
  • Pricing schemes: Under flat pricing, users pay a subscription fee; two-tier pricing offers multiple usage options; volume pricing charges per 3G unit; congestion pricing varies unit prices by time and cell.The schemes differ in price granularity and whether users subscribe or control traffic volume.
  • Offloading indicators: Traffic offloading is measured by aggregate and peak 3G traffic ratios, κavg and κpeak.These indicators quantify overall and peak-time cellular traffic remaining after WiFi offloading.
  • Offloading indicators: Both κavg and κpeak decrease as users tolerate greater delay because more traffic can be transmitted through WiFi.The aggregate ratio captures total cellular traffic, while the peak ratio captures peak cellular load.
  • Network regimes: Opt-saturated and opt-unsaturated regimes distinguish whether peak 3G traffic reaches capacity at the revenue-maximizing equilibrium price.The distinction matters because traffic volume and market behavior affect the analysis differently.
  • Feasibility: Feasible prices must yield positive provider revenue and keep expected 3G traffic below capacity at every time.The feasible set is P = {p | R(p) > 0, Y(t; p) ≤ C3g, ∀t ∈ T}.

B. Flat pricing

Under flat pricing, the paper characterizes feasible and equilibrium prices and proves that delayed offloading can benefit users and the provider, with mechanisms depending on network saturation.

  • Flat-pricing model: Flat pricing charges a fixed fee regardless of a subscriber’s 3G traffic, so subscribing users generate traffic equal to their demand.Users’ willingness to pay and demand determine subscription and provider revenue.
  • Equilibrium pricing: The feasible price set lies below pmax, the price at or above which no user subscribes, and equilibrium prices must also satisfy provider rationality and capacity constraints.The revenue function is unimodal over the relevant price interval.
  • Economic gain: If η < (κavgΦmax^(1−θ))^-1, delayed offloading increases every subscriber’s net utility and raises equilibrium provider revenue when κpeak or κavg decreases in the relevant regime.The theorem covers decreasing κpeak in opt-saturated networks and decreasing κavg in opt-unsaturated networks.
  • Opt-saturated mechanism: In opt-saturated networks, lower κpeak creates capacity that the provider uses to attract subscribers through a lower flat fee, increasing revenue when subscriber growth exceeds the price reduction.The equilibrium price decreases as κpeak decreases.
  • Opt-unsaturated mechanism: In opt-unsaturated networks, lower κavg reduces network cost substantially, raising revenue even when additional subscribers do not increase drastically.The provider’s revenue mechanism therefore differs from the capacity-release mechanism in the opt-saturated case.

C. Volume pricing

Under volume pricing, users pay in proportion to 3G traffic and choose traffic volume to maximize net utility. The model characterizes equilibrium prices and shows that delayed offloading benefits users and the provider under both opt-saturated and opt-unsaturated conditions.

  • Volume pricing: Users pay proportionally to their 3G traffic volume and choose traffic to maximize net utility for a given unit price.The analysis assumes homogeneous per-user and per-time delay profiles and WiFi connection probabilities for tractability.
  • Economic implications: Theorem 4.2 states that offloading is economically beneficial for users, the provider, and the regulator.This conclusion summarizes the economic implications established for volume pricing.
  • Equilibrium price: The provider’s revenue function is unimodal, and the feasible price set is non-empty and connected.The equilibrium analysis distinguishes opt-saturated and opt-unsaturated network conditions.
  • Economic gain: Delayed offloading increases every user’s net utility, provider revenue, user surplus, and social welfare as κpeak or κavg decreases, depending on network saturation.The relevant parameter is κpeak in the opt-saturated case and κavg in the opt-unsaturated case.
  • Opt-saturated case: In the opt-saturated case, reduced κpeak lowers the equilibrium price because offloading creates extra 3G capacity and attracts more traffic.The provider lowers the unit price to obtain higher revenue from additional traffic.
  • Opt-unsaturated case: In the opt-unsaturated case, reduced 3G traffic lowers costs, while the provider raises price without reducing total traffic when payment per unit traffic remains unchanged.The resulting cost reduction is identified as the main factor behind revenue growth.

V. TRACE-DRIVEN NUMERICAL ANALYSIS

The numerical analysis combines real traces with projected 2015 traffic statistics to evaluate delayed WiFi offloading across capacities, user demands, WiFi connectivity, mobility, and delay scenarios. It models 31 cells and 31,000 users using measured or externally specified parameters.

  • Experimental setup: The experiment models 24 hourly time slots, 31 base-station cells, 31,000 users, and cellular capacities of 8 Mbps for 3G and 32 Mbps for 4G.The 4G capacity is projected to be about four times the 3G capacity.
  • Traces: WiFi connectivity is measured from 93 iPhone users in Korea, whose locations and time-varying WiFi connections were recorded every three minutes for two weeks.The trace captures accessible open or authorized WiFi access points.
  • Traffic demand: Traffic demand follows an upper-truncated power-law distribution with exponent σ = 0.57 and monthly averages ranging from 93 MB to 5.2 GB.The projected 2015 average smartphone traffic used for comparison is 1.3 GB per month.
  • Trace processing: The analysis uses WiFi contact probabilities, cell-level mobility statistics, and repeated individual traces to generate data for the modeled user population.Cell-level mobility supports capacity constraints and congestion pricing, while the 93-user traces are reused to generate N users.
  • Delay scenarios: Delay tolerance is evaluated through no-deadline, short, medium, and long scenarios across Video, Data, P2P, and Audio traffic classes.The numerical study considers both uniform assignment of one scenario to all users and fixed proportions across scenarios.

B. Results

Delayed WiFi offloading increases provider revenue and user benefits across pricing, traffic, capacity, and delay-tolerance scenarios. The gains vary with pricing granularity, traffic saturation, and users’ delay disutility.

  • Revenue effects: 61-152% revenue increase occurs with delayed offloading under flat pricing, compared with 21-43% under volume pricing.Revenue under volume pricing remains higher in absolute terms, but delayed-offloading gains are larger under flat pricing.
  • Revenue effects: 21-43% revenue gain from delayed offloading is comparable to the gain from upgrading the network from 3G to 4G.Both gains are small when traffic demand is low relative to capacity.
  • Pricing and surplus: 15-44% lower flat fees and 28-59% lower volume payments accompany increased subscription or user surplus under opt-saturated demand.The reported case uses average demand of 1.5 GB/month.
  • Pricing and surplus: Two-tier and congestion pricing increase revenue relative to flat and volume pricing, but their gains shrink as more traffic is offloaded.Greater pricing granularity gives the provider more control over the market.
  • Delay tolerance: Revenue gain and delayed-offloading adoption both decrease as delay disutility increases, reaching zero adoption above 40% disutility.More than 50% revenue gain remains for disutility below 15% with long delays and below 10% with short delays.
  • Additional benefits: WiFi offloading also reduces transmission energy, with prior work reporting 50-60% savings for a one-hour delay.The paper notes this energy benefit but does not include it in the economic model.

A. Proof of Proposition 4.1

The proposition characterizes provider revenue as unimodal in price and derives the connected feasible-price set under provider rationality and cellular-capacity constraints. The resulting optimum is unique and may be capacity-saturated or unsaturated.

  • Revenue shape: R(p) is unimodal because it is concave below a threshold and convex above it, with a unique stationary price ˆp.The derivative changes sign from positive to negative at ˆp.
  • Feasible prices: P = E ∩ F is connected because capacity feasibility E and positive-revenue feasibility F are each connected price sets.The capacity constraint yields a lower price boundary pmin, while revenue feasibility yields a lower boundary pz.
  • Equilibrium cases: The unique equilibrium price is p0 when revenue decreases throughout the feasible set, and the network is opt-saturated with A(p0) = C3g.This occurs when the unconstrained revenue maximizer lies at or below the feasible-price boundary.
  • Equilibrium cases: When R′(p0) > 0, the unique optimum satisfies ˆp > p0 and A(ˆp) < C3g, so the network is opt-unsaturated.The unconstrained revenue maximum lies inside the feasible region rather than at its lower boundary.
  • Parameter effects: Decreasing κavg increases the feasible-price set and the maximum provider revenue.The revenue-positive set expands while the capacity-feasible set remains unchanged with respect to κavg.

B. Proof of Theorem 4.1

The theorem links lower offloading indicators to lower prices and higher user utility within the model. It shows that reduced κavg expands feasible pricing and raises revenue, while reduced κpeak lowers the optimal payment per traffic unit.

  • User utility: The net utility of a subscriber increases as the optimal price p⋆ decreases.The result follows from the subscriber’s net-utility expression and the proposition’s price comparative statics.
  • Effect of κavg: Net utility and user surplus increase as κavg decreases because the flat fee decreases.The feasible price set also expands as κavg decreases.
  • Effect of κavg: The feasible price set Pκavg is enlarged, or remains unchanged, as κavg decreases, and maximum revenue increases.The capacity-feasible set does not depend on κavg, while the positive-revenue set expands.

C. Proof of Proposition 4.2

The proposition proves that provider revenue is unimodal in price, characterizes feasible prices, and distinguishes optimal saturated from unsaturated networks. It also derives how optimal prices and payments respond to offloading parameters.

  • Revenue shape: R(p) is unimodal for p > η because its derivative changes sign once at ˆp.The derivative is positive below ˆp, zero at ˆp, and negative above it.
  • Feasible prices: The feasible-price set is P = (p0, ∞) when p0 = η and P = [p0, ∞) when p0 = pmin.Here p0 = max{pmin, η}, with pmin determined by the capacity constraint.
  • Optimal network state: When R′(p0) ≤ 0, p0 is the unique optimal price, the network is opt-saturated, and A(p0) = C3g.Revenue is nonincreasing throughout the feasible set in this case.
  • Optimal network state: When R′(p0) > 0, ˆp is the unique optimum and A(ˆp) < C3g, so the network is opt-unsaturated.The conclusion holds whether p0 equals η or pmin.
  • Parameter effects: The optimal per-traffic payment decreases as κavg decreases, while actual payment per unit traffic increases as κavg decreases.The proof distinguishes the optimal price parameter from the product ˆp(κavg)κavg.

D. Proof of Theorem 4.2

The proof establishes how pricing and traffic parameters affect user utility, user surplus, and provider revenue. Lower prices and lower average or peak cellular traffic increase the relevant economic outcomes under the stated network conditions.

  • Lowering the price increases a user's net utility.
  • In an opt-saturated network, the optimal price depends on peak traffic, and the proof shows revenue increases as peak traffic decreases.
  • Decreasing average cellular traffic increases both net utility and user surplus.
  • Decreasing average cellular traffic increases maximum provider revenue.
  • Under a reduced-traffic transformation, the corresponding user traffic remains unchanged while 3G traffic and revenue are compared across the original and new settings.
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