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Analytical Model of Failure in LTE Networks

Maryam Monemian, Pejman Khadivi, Maziar Palhang

Department of Electrical and Computer Engineering

Isfahan University of TechnologyIsfahan, 84156-83111, IRAN

m.monemian@ec.iut.ac.ir

pkhadivi@ec.iut.ac.ir

palhang@cc.iut.ac.ir

Abstract Recently, Long-Term Evolution or LTE for 3G has

been introduced to improve service provisioning for mobile

network subscribers. This service improvement includes

improvements in setup delay and data rates in different services.

In this paper, one of the existing architectures, proposed for

LTE, is evaluated. Then, probable faults in this architecture and

their impacts on network services are investigated through a

causality graph. This graph is used to calculate service failureprobabilities in mobile networks. Also, the impact of failure of

one of the serving nodes in the LTE architecture is evaluated

through an analytical model. Simulation results support the

arguments of the paper.

KeywordsLTE Architecture, Failure, Handoff, CausalityGraph, Repair

I. INTRODUCTIONIn modern world, the need for making communication

between people is strongly felt and people need to access

information regardless of their locations. In other words, the

necessity of making communication in each moment orlocation is deeply felt. This is the important concept of always

best connected networking. These requirements are met only

with a reliable and efficient wireless networking.

With respect to the increasing number of subscribers for

mobile and wireless networks, enhancement in network

services with suitable costs is an important requirement. For

this reason, 3GPP (Third Generation Partnership Project) has

introduced LTE to decrease delay in setup process and

increase data rates in services [1], [2]. In LTE the above

purposes are provided using different approaches, such as

multi-antenna or OFDM techniques. Generally the LTE goals

include the optimization of frequency spectrum efficiency, the

possibility of providing higher data rates and delay reductionin setup process [1].

Mobile and wireless networks have unique features which

are not found in the wired systems [3], [4]. For example,

limited channel capacity, limited bandwidth and frequency

spectrum, noise and interference are the most challengingfactors in cellular networks. Also, the failure of different

serving nodes in the network can make disorder in network

performance and causes call blocking and connection failures.

In this paper, different failures in LTE architecture and

their impacts on network services are verified. In other words,

at first the failures of different nodes in LTE architecture are

verified. Then, the impacts of these failures on the network

services are evaluated through a causality graph.

Similar works have been reported about verifying mobile

networks failures and optimizing those networks reliability. In

[5] different kinds of failures in wireless networks and their

impacts on network performance have been evaluated andParameters such as MTTR (Mean Time To Repair) and

MTBF (Mean Time Between Failure) are considered for each

node in the network topology. Also, it is reported that having

redundancy for nodes is a method to enhance reliability in

end-to-end connections [5].

In [6] three important metrics have been used to verify theimpact of failures on a network. These metrics are failure

frequency, failure duration and the number of subscribers

which have been affected from the failures.

In [7], it is discussed that main metrics which affect the

performance of wireless cellular systems, are the probability

of an ongoing call being dropped due to a handoff failure and

the probability of a new call being blocked due to thetemporary unavailability of an idle channel. In order to

overcome this problem, cellular networks with failures and

recovery are modeled and a Markov Reward Model is used to

represent such a system with handoffs [7].

The remainder of the paper is organized as follows. Insection II, the current 3GPP Release 6 architecture and a

suggested architecture for LTE are introduced. In section III

causality graph is defined and is used to show causal

relationships among different network failures and services. In

section IV the impact of failure of one of the serving nodes inthe network architecture on the network performance is

analyzed with a Markov model. In section V the proposed

Markov model is evaluated through simulations. Section VI isdedicated to concluding remarks.

II. LTEARCHITECTUREIn this section, architecture for LTE is introduced [1], [2].

The architecture which is considered for 3GPP Release 6 is

shown in Figure 1(a). In this architecture, NodeB acts as a

base station. The RNC (Radio Network Controller) handles

radio resource management, mobility management, transport

network optimization and call control. It also controls several

NodeBs. The SGSN (Serving GPRS Support Node) handles

Proceedings of the 2009 IEEE 9th Malaysia International Conference on Communications

15 -17 December 2009 Kuala Lumpur Malaysia

978-1-4244-5532-4/09/$26.00 2009 IEEE 821

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encryption and compression of transmitting data, IP packets

routing and data session management. The GGSN (GatewayGPRS Support Node) acts as a gateway between the wireless

GPRS network and other networks such as Internet or any

private network.

In order to meet LTE purposes, some changes can be made

in the architecture of Figure 1(a). For example, the SGSN,

GGSN and RNC nodes can be merged into one node to

decrease setup delay and provide services with lower prices.This new node is called ACGW (Access Core Gateway). The

architecture is shown in Figure 1(b). Hence, the number of

nodes in the path of users' requests is decreased and the

amount of delay and the cost of services is reduced [1].

III.CAUSALITY GRAPH FORLTEIn the architectures of Figure 1, different failures may occur

and affect the performance of the network. There are different

techniques which can be used for fault localization based on

observed symptoms [8]. One of these techniques is FPM or

Fault Propagation Model Technique, that includes graphs toshow existing failures in the system and appears as

dependability or causality graphs [8]. In this paper, the

causality graph is used to show probable failures in the LTE

architecture and explain causal relationships between them

and network services.

Definition: A causality graph is a directed acyclic graph,GC(E,C), whose nodes E correspond to events and whose

edges C describe cause-effect relationships between events.

An edge (ei, ej) Cshows that event ei causes event ej and is

denoted with eiej [8].

, , (1)In what follows, a causality graph is introduced for LTE

architecture. For simplicity, only one cell is considered. The

following notations are used:

Fig. 1 a)Current architecture for 3GPP Release 6. b) A suggested architecture

for LTE.

Fig. 2 Causality graph for LTE architecture.

N: NodeB failure

L: Failure in the link between NodeB and ACGW.

A: Failure in the ACGW node.

M: Failure in the mobile device.

BW: Bandwidth shortage.

In what follows, two user requests, which may be affectedby the above failures, are investigated. Failure in call service

is shown with F1, and failure in data service or making

connection with other networks is illustrated byF2.

Obviously, if there is a failure in NodeB, or if it can not

work due to any problem, subscribers are not able to use call

or data services. Therefore, the edge between F1 and N, and

the one between F2 and Nin the causality graph, are marked

with and , respectively. As it wasmentioned before, the ACGW should perform the GGSN,

SGSN and RNC functions; Hence, the ACGW failure affects

on both call and data services and the edge betweenF1 andA,

and the one betweenF2 andA, are marked with and, respectively. Also, the failure of the link betweenACGW and NodeB probably affects on both data and call

services. Therefore, the edge between F1 and L, and the one

between F2 and L, are marked with and ,respectively.

Bandwidth shortage in a cell may prevent the NodeB from

assigning channel to users and hence, call and data services

are affected. Then, the edge betweenF1 andBW, and the one

between F2 and BW, are marked with and , respectively. Also mobile device failure maycause failure in making call or data connection. Therefore, the

edge between F1and M, and the one between F2 and M, are

marked, with and , respectively.Considering above cases the causality graph is shown in

Figure 2. The probability of unsuccessfulness in making call

connection,P(F1), can be calculated using the causality graph

and is given by (2).

(2)

In (2),Ais are different failures which affect call service. In

other wordsAi can be one of theBW,M,N,L, orA. Similarly,the probability of unsuccessfulness in making data connection,

P(F2), can be calculated using the causality graph and is given

by (3).

(3)

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Figure 3. A Markov model showing number of users which receive service

and users in the queue.

In (3),Ais are different failures which affect on data service.In other words Ai can be one of the BW, M, N, L, orA. If

and and different failure probabilitieshave certain values,P(F1) andP(F2) can easily be calculated.

IV.ANALYTICAL MODEL FORNODEBFAILUREIn this section, the impact of failure of NodeB on the

networks behavior is modeled with a Markov process. The

aim is to investigate the effects of NodeBs failure on the

network performance and the number of users which lose theiractive connections. For simplicity it is assumed that handoff

requests are handled similar to new connection requests.

The Markov model of the system is illustrated in Figure 3.

In this figure, the state (n, m) shows that n users are in waitingqueue to receive service and m users are receiving service. It

is also assumed that NodeB has at most Nchannels to servethe requests. If there is a free channel among those Nchannels,

then NodeB uses that free channel to serve a connection

request and assign it to a subscriber. If all the Nchannels are

busy to serve the users and a connection request arrives to the

NodeB, this request is assumed to go to the waiting queue.This case shows the state, which user begins to reconnect to

receive the channel after unsuccessful try and it is assumed as

a kind of being in a queue.

Assume that arrival of connection requests to a cell is a

Poison process with rate . Also, it is assumed that the number

of connection requests in a cell can be unlimited.In what follows, we assume that the failure of NodeB has

an exponential distribution with rate f. Note that NodeB

failure means that no channel can serve the requests. Also, it

is assumed that after any failure, NodeB is repaired after a

random duration of time with exponential distribution with

rate rand no user in the queue relinquishes from the service.First, let us define , as in equation (4):

(4)

where, , is the arrival rate to the cell, f, is the failure rate of

the NodeB, and r, is the corresponding repair rate. Hence, theprobability of having n users with active connection (being

served by NodeB), with no subscriber in waiting queue is

equal toP(0,n):

0, !

0,0 1 (5)

where, , is the service rate of the NodeB, and N is thenumber of total channels in the cell. Note that P(0,0) shows

the probability of the state, that the system is empty (with no

user being served or in the queue). Also, we have:

, 0 0, 1 (6)

and

, !

0,0 ; 1 (7)

The probability that n + N users are in the queue, while

NodeB is in the failure is given by (8):

, 0 !

0,0 ; 1 (8)

The average number of subscribers in the queue, NQ, may

be determined based on the above equations:

, 0

,

, 0

(9)

Also, the average of waiting time in the queue, W, is

calculated using equation (9) and the Littles formula [9]:

(10)

V.NUMERICAL RESULTSIn order to evaluate the proposed model, a simulator has

been developed to solve the Markov chain of Section IV. By

solving this Markov chain, different probabilities of being in

different states could be determined. Based on theseprobabilities, one can determine the expected values of

different system parameters. In this section, the numerical

results are described. The duration of simulation is equal to

1,000,000 units of time.

Numerical results are shown in Tables I and II and Figures

4 and 5. In Tables I and II, the average number of subscribersin the queue is calculated for different failure and repair rates.

As it is expected, the average number of subscribers in the

queue is increased with increasing the value off. In Table I

the values of , , and rare constant. NQ is determined for

different values off. In Table II the values of , , f are

constant and each time ris multiplied by two. Approximately,when ris multiplied by 2, the average number of customers in

the queue is halved. Also, with any reduction in r, the number

of users in the queue is increased and consequently the

average waiting time is increased according to (10). Based on

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the culture and the social behavior of subscribers, people in

different societies may wait for a different period of time forthe network restoration. Hence, there must be a lower bound

for suitable repair (or restoration) rate, r, of the network.

In Figure 4(a), P(0,0) is calculated from the analytical

model for different values ofs. This is also compared with

the numerical results generated by the simulator. It is almost

clear that P(0,0) is decreased with increasing of. Also, the

curves are approximately close together. Similar results areillustrated in Figure 4(b), for P(0,0) versus . Figure 5

demonstrates variation ofP(0, 4) for different values of and

. It is clear from this figure that P(0,4) is increased with

increasing of and is decreased with increase in.

VI.CONCLUSIONSIn this paper, different failures in the suggested architecture

for LTE were verified and the impact of them on network

services was evaluated through simulation and analytical

models. NodeB failure was modeled with an exponential

distribution with rate f. It was observed that f affects on theaverage number of users in the waiting queue. Also,

simulation results show that repair rate (r) should be large

enough, in order to have a suitable average waiting time.

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TABLEI

NQ CHANGING WITH FAILURE RATES (f).

TABLEII

NQ CHANGING WITH REPAIR RATES (r).

(a)

(b)

Fig. 4 a)P(0,0) changing with different values for. b)P(0,0) changing with

different values for.

(a)

(b)

Fig. 5 a)P(0,4) changing with different values for. b)P(0,4) changing withdifferent values for.

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

lambda

P(0,0

)

Simulation model

Analytical model

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90.2

0.25

0.3

0.35

0.4

0.45

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P(0,0

)

Simulation Model

Analytical Model

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90.02

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P(0,

4)

Simulation Model

Analytical Model

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

0.005

0.01

0.015

0.02

0.025

0.03

0.035

mu

P(0,

4)

Simulation Model

Analytical Model

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