System Model

In this section, we first describe the network model and the offloading environment. After- ward, we explain the task computation, communications, and queue models.

System Framework

We consider a two-layer architecture for VEC. By U = {u1, . . . , ui, . . . , uN}, we represent

the set of heterogeneous Edge Units (EUs) in the first layer. All the EUs have certain computational and storage capabilities. The second layer includes M types of wireless networks, each with MjBSs [129]. F = {Fmj}

m=1,...,M

j=1,2,...,Jmshows the set of BSs, where m is

the index for the network and j is the index for the BS of that specific network. Every EU can communicate with at least one BS by means of cellular-based communication.

Each BS is equipped with a number of computational servers and therefore can process different tasks. In general, the BSs have higher computational capabilities and coverage area

200 400 600 800 1000 1200 1400 1600 1800 2000 Number of FNs 1.6 1.8 2 2.2 Delay [s]

Low Capacity Ideal Low Capacity D&V Low Capacity D&V&T

W

High Capacity Ideal High Capacity D&V High Capacity D&V&T

W

Fig. 4.7 Average task delay with relaying through 11 fixed F-APs

compare to EUs. They can aggregate the EUs’ traffic requests and process the offloaded tasks. The BSs of each network type are homogeneous in the sense that they have the same computational and coverage characteristics. In contrast, the type of BSs varies from one network to another.

We consider an urban scenario as shown in Fig. 4.8, where the vehicles act as EUs. Each vehicle i moves with some velocity vithat is selected uniformly at random. The vehicles can

move from left to right or in the opposite direction, depending on their location. The speed and the direction of each vehicle remain fixed through time [126, 131]. An outage occurs if an offloading vehicle is not able to receive the result of the offloaded task due to its mobility, i.e., due to the short sojourn time.

In heterogeneous wireless networks, the networks of different sizes overlap while covering the entire area. In addition to different coverage and computational capacities, heterogeneous networks also face different traffic demands, therefore different congestion probabilities. Another important issue is the packet loss, as some times an EU is not able to receive the task result due to a shortage in the sojourn time.

Based on the discussion above, the offloading decision in dynamic vehicular environments is twofold. First, an EU selects the optimal network to offload its task, based on the probability

Fig. 4.8 Partial offloading mobile urban scenario.

of congestion. Afterwards, it selects a BSs in the selected network that guarantees the reception of the result of the offloaded task.The goal of the this work is to address the joint delay and outage minimization problem by a suitable selection of the network and BS for computation offloading.

Task Computation and Communication Model

The computational time for the lth task generated by the EU is defined as:

T_cl(t) =    O·δl(t) ηi local computation O·δl(t) η_{m j} otherwise (4.24)

where O represents the number of operations required for computing one byte, δl(t) is the

where rupmj(t) is the up-link data rate of the link between the EU and the mjth BS at time

instant t. Later the result of the processed task should be sent back from the mjth BS to the

EU, leading to a reception time as

T_rx,ml _j(t) = ωl rdl

mj(t)

(4.26)

where rdl_mj(t) is the down-link data rate and ωl is the size of the result of processing.

In urban scenarios, there is often no line-of-sight due to the dense presence of buildings. Moreover, on a highway, the trucks on a communication path may introduce significant signal attenuation and packet loss [150]. Hence we assume that cellular networks have different channels so that there is no inter-cell interference, whereas the users might confront intra-cell interference due to the signal attenuation. Therefore, we make the following assumption. Assumption 1. A user i inside a cellular network experiences independent and identically distributed interference signals caused by other users. However, different cells use different channels so that there is no inter-cell interference.

Focusing on a specific time instant when user i is inside the mjth cell, we define Ii,ι = 1,

where i, ι ∈U,i ̸= ι, if the ith EU is interfering with ιth EU. Thus the interference received by the ith EU yields

I_mi _j=

_∑

ι

Ii,ιβι ,mj(t)P

mj

tx (4.27)

where βi,mj(t) is the path loss attenuation factor of the channel, which is a function of

the distance, shown as di,mj(t), between the BS and the vehicle. Moreover, P

mj

tx is the

transmission power of the mjth BS. The distance between the ith EU and the mjth BS is

given by [134, 151]

d_i,mj(t) =qh2

mj+ |ymj− yi(t)|2+ |xmj− xi(t)|2 (4.28)

where {xi(t), yi(t)} and {xmj, ymj} are, the position of the ith EU at time t and the mjth BS,

Let Bjrepresent the bandwidth of the leased channel for the cellular network. By Shannon

capacity formula, the transmission rate in the up-link from the ith EU to the mjth BS at time

instant t yields r_mup j(t) = Bjlog2 1 + βi,mj(t)P i tx I_mi _j+ σ2 ! (4.29) where P_txi is the transmission power of the ith EU. Moreover, σ2is the noise power defined as σ2= NTBj, where NT is the noise density. Due to the channel reciprocity, the reception

rate of the results in the down-link, i.e., from the mjth BS to the ith EU, can be similarly

calculated by using the BS’ transmission power. We assume that the channel is quasi-static during transmission and reception period.

Queue Model

We observe the arrival processes in networks from a bit-level perspective, and consider a Poisson-Exponential queuing model, as extensively used in the literature [152]. The server has a buffer large enough to queue all packets. The task arrival to the BSs belonging to the mth network follows a Pois(λm) distribution. Moreover, the service time follows Exp(µm)

distribution. Therefore, the waiting time of the lth task offloaded to Fmj is given by

T_wl m j(ϑt) = ϑt−1

∑

where ϑt is the queue length of the mjth BS at time instant t, and κ represent the index of

the nodes in the queue. Hence, ϑt ∼ λm and Tclκ ∼ µm. As a result, (4.30) represents the

task waiting time in the BS of any network. The distribution’s characteristic (arrival- and departure rate) for the BSs belonging to each network is the same.

We are interested in analyzing the behavior of a single EU in a vehicular environment when it makes offloading decisions. There are mainly two phases for an offloading scheme: (i) Network selection based on congestion characteristics; and (ii) BS selection in the selected network. In the following, we describe our proposed network and BS selection procedures.