MUTUAL EXCLUSION IN CYBER-PHYSICAL SYSTEMS

Sumeet Gujrati and Gurdip Singh

Computing and Information Sciences, Kansas State University, Nichols 234, Manhattan, U.S.A.

Keywords:

Cyber-physical Systems, Resource Allocation, Mutual Exclusion.

Abstract:

Distributed computing problems such as mutual exclusion have been studied extensively for traditional dis-

tributed systems. In traditional systems, a strict layered approach is taken wherein a set of users (application

processes)

U1, . . . ,Un

is layered on top of a mutual exclusion algorithm with processes

, . . . , P

. User

interacts with process

to request access to resources which are modeled as tokens, and users rely entirely

on mutual exclusion algorithm to regulate access to the resources. In a cyber-physical system, users (physical

entities) may themselves possess capabilities such as sensing, observing and mobility using which they may also

attempt to locate physical resources such as wheelchairs. Thus, a mutual exclusion algorithm in a cyber-physical

system must contend with the behavior of users. This paper proposes a graph-based model for cyber-physical

systems which is used to describe mutual exclusion algorithm as well as user behavior. Based on this model,

we present several solutions for the mutual exclusion problem. We have also conducted an extensive simulation

study of our algorithms using OMNeT++ discrete event simulation system.

1 INTRODUCTION

Cyber-physical systems are often formed as a result

of existing physical systems being instrumented with

cyber-infrastructure with the intention of aiding tasks

which are being accomplished by traditional (perhaps

manual) techniques. For example, consider a health

care facility where users (

e.g.

, hospital staff) share

resources (

e.g.

, wheelchairs, IV pumps) located in dif-

ferent parts of the facility. This facility may be using

established traditional techniques to locate and share

resources (

e.g.

, depositing free resources at a central

or a set of known locations). However, for more ef-

ﬁcient operation, the resources can be instrumented

with sensing devices to track their location and usage,

and the information made available to potential users.

(Wieland et al., 2007) describes a similar smart factory

environment where context data (location and usage)

regarding tools, machines, transport carts, and spare

parts is made available via RFID tags to aid in locating

the nearest tools/machines available to do a task. Sim-

ilar systems have been discussed in various contexts

such as locating empty spaces in parking lots (Chin-

rungrueng et al., 2007), room reservation in buildings

(Conner et al., 2004) and smart building operations

(Liu et al., 2010).

One central issue in many application scenarios

such as discussed above is the use of resources in an

exclusive manner. In this paper, we study the problem

of mutual exclusion in cyber-physical systems where

users need exclusive access to physical resources. In

a traditional distributed system (TDS), a mutual ex-

clusion algorithm is typically modeled as a set of pro-

cesses

, . . . , P

, where

executes on node

, and a

strict layered structure is used wherein user

inter-

acts with

to gain access to a resource. The access of

the resources in a TDS is completely regulated by the

mutual exclusion algorithm.

PhyA

Figure 1: Cyber-infrastructure superimposed on a physical

system.

In a cyber-physical system (CPS), the cyber- infras-

tructure may have been superimposed on an existing

physical system (Figure 1). In such cases, a distributed

algorithm may have to contend with direct interactions

between the users and the resources. This introduces

several aspects in the context of the mutual exclusion

problem which are not addressed in a TDS. First, the

users may not be passive entities – that is, in addi-

Gujrati S. and Singh G..

MUTUAL EXCLUSION IN CYBER-PHYSICAL SYSTEMS.

DOI: 10.5220/0003834800730079

In Proceedings of the 1st International Conference on Sensor Networks (SENSORNETS-2012), pages 73-79

ISBN: 978-989-8565-01-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

tion to requesting the cyber-infrastructure to locate

resources, the users may actively look for resources

on their own. For example, in Figure 1, in addition

to asking

to locate a resource, if

observes that

resource

is available, it may acquire

without

waiting for a response from

, Second, in a TDS, the

state of a resource is controlled by mutual exclusion

algorithm. In a CPS, however, the users may indepen-

dently observe and change the state of the resources.

This, for instance, may cause scenarios wherein a user,

say

in Figure 1, may start using

even though mu-

tual exclusion algorithm may think that it is free and

may reserve it for another user (as there may not be a

way to ”lock” a physical resource). Third, physical re-

sources may be mobile so that they may be acquired at

one location and released at another (

e.g.

, a wheelchair

may be freed at a different location). This is different

from the view taken in a TDS where a resource (

e.g.

abstracted as a token) is released by the user at the

same node where it was acquired.

We ﬁnd that the aspects in a CPS discussed above

can have a signiﬁcant impact on the design of mutual

exclusion algorithms. Several other problems such

as distributed algorithms for creating globals states

in intelligent construction sites (Rajamani and Julien,

2010), event ordering (Romer, 2003; Kaveti et al.,

2009) and termination detection (Bapat and Arora,

2008; Kurian et al., 2009) have been studied for CPSs.

Although existing research discussed above has ad-

dressed some aspects of interactions between cyber-

infrastructure and the users, the problem in the context

of mutual exclusion has not been addressed. The con-

tribution of this paper is three-fold:

•

We propose a model which views a CPS as a triple

(CyS, PhyS, Int)

, where

CyS

models the cyber-

infrastructure superimposed on physical system

modeled as

PhyS

, and

Int

captures the interac-

tions between them. We call

CyS

and

PhyS

cyber-

subsystem and physical-subsystem respectively.

•

We propose a set of algorithms based on the pro-

posed model for the mutual exclusion problem.

Each algorithm has two components, one describ-

ing the behavior of the users in

PhyS

and the other

describing the mutual exclusion algorithm (or cy-

ber algorithm) in

CyS

. Each combination of user

behavior and cyber algorithm yields a different

CPS algorithm.

•

We have conducted an extensive simulation study

of proposed algorithms using OMNeT++ (Varga,

2001) which simulates both user behavior and cy-

ber algorithm.

This paper is organized as follows. Section 2 dis-

cusses a model of TDSs and Section 3 presents the

extension for a CPS. Section 4 discusses solutions to

the mutual exclusion problem for CPSs. Section 5 dis-

cusses simulation and results, and Section 6 concludes

the paper.

2 TRADITIONAL DISTRIBUTED

SYSTEMS

A traditional distributed system (TDS) is modeled as

a graph

= (CE, E)

, where CE is a set of cyber en-

tities (computing platforms) and E is a set of edges (or

communication links)

i j

between two cyber entities

and

(Chandy and Lamport, 1985). Each

V ∈ CE

has a set of processes, denoted by

V.processes ∈ CP

running on it. Processes executing on cyber entities

communicate via the communication links to interact

with each other.

A mutual exclusion algorithm for a TDS typically

models a physical resource (

e.g.

, a printer) as an ab-

stract object and provides users with an interface with

functions to request, acquire and release a resource,

and ensures that at most one user is granted access

to a resource at a time. Mutual exclusion algorithms

have been studied extensively (Dijkstra, 1965; Dijk-

stra, 1971; Lynch, 1980; Reif and Spirakis, 1982) for

both shared memory and message passing systems. In

the more general k-mutual exclusion problem, at most

k processes are allowed to be in critical section at the

same time (Bulgannawar and Vaidya, 1995; Makki

et al., 1992; Srimani and Reddy, 1992; Walter et al.,

2001; Raymond, 1989).

In (Walter et al., 2001), a k-mutual exclusion al-

gorithm, which is referred to as the KRL algorithm,

was proposed for wireless ad hoc networks. As one

of our solutions is based on the KRL algorithm, we

discuss this algorithm in more detail in the follow-

ing. In the KRL algorithm, each node i maintains a

data structure

height

, which is a three-tuple

, h

, i)

Edges are directed from higher height nodes to lower

height nodes based on lexicographic ordering. For

example, if

height

= (2, 3, 0)

and

height

= (2, 2, 1)

then

height

> height

and the edge will be directed

from node 0 to node 1. KRL algorithm maintains n

nodes and k tokens, where

k < n

. For all nodes i,

height

is initialized so that the directed edges form

a directed acyclic graph (DAG) such that every node

has a directed path to some token holder and every

token holder node i has at least one neighbor n such

that

height

> height

. When a user at node i wants to

enter the critical section, it makes a request which is

enqueued by

in its local queue

. When

receives

a request from neighbor

and

height

> height

enqueues the request in

. If

is a non-token holding

SENSORNETS 2012 - International Conference on Sensor Networks

node and Q

is empty when the request is received, P

sends a request to its neighbor with the lowest height.

Hence, requests propagate via lower height nodes to

the token holders. If

has (or receives) a token, it

dequeues the ﬁrst request from

. If this request is

from its own application process,

gives permission

to its application process; else, it sends the token to its

neighboring node whose request it just dequeued.

3 CYBER-PHYSICAL SYSTEMS

We model a CPS as a triple

(CyS, PhyS, Int)

CyS

deﬁned in the same way as in a TDS. PhyS is deﬁned

as a pair (

PE, G

), where PE is the set of physical

entities and

is a graph (

PA, RE

), where PA is a set

of physical areas and RE is the set of reachability edges.

An edge

i j

∈ RE

represents the fact that a physical

entity can move directly from area

PhA

to area

PhA

A reachability edge

i j

between

PhA

and

PhA

analogous to a communication link

i j

between two

cyber entities

and

. For example in Figure 1, since

there is a doorway connecting

PhA

and

PhA

, there is

a reachability edge between them. We further partition

PE into two sets, AE and RS, where AE is a set of

active entities and RS is a set of resources. Active

entities are the users of the system and can perform

actions on their own (

e.g.

, hospital staff) and may use

the resources (e.g., wheelchairs) in the set RS.

We model each area

PhA ∈ PA

by two abstract

variables, PhA.ae and PhA.rs, which denote the set

of active entities and set of resources respectively cur-

rently located in area PhA. Similarly, we model the

state of a resource

r ∈ RS

by a variable r.state, which is

either free or busy. We assume that these abstract vari-

ables are updated automatically based on the actions

of active entities. For instance, if

U ∈ PhA.ae

, and

U moves out of the area PhA, then the state variable

PhA.ae is automatically updated so that U is removed

from PhA.ae. Similarly, when U enters a new area, the

corresponding state variable is updated to include U.

We assume a similar update happens for PhA.rs when

resources are moved between areas.

3.1 Interaction between Entities

This section deﬁnes the possible actions by active enti-

ties and interactions between the cyber- and physical-

subsystems:

• Sensing.

If a cyber entity

V ∈ CE

has the capa-

bility of sensing the presence of physical entities in an

area

PhA

, then we model this by allowing processes in

V.processes

to read

PhA.ae

and

PhA.rs

. Furthermore,

we also allow these processes to read

r.state

for each

resource r ∈ PhA.rs.

• Actions Performed by an Active Entity.

use the following actions to describe the behavior of

an active entity U ∈ AE:

•

Move(PhA) is an action which represents U mov-

ing from its current physical area to another phys-

ical area

PhA ∈ PA

, and is possible only if there

exists a reachability edge from its current physical

area to PhA.

•

Observe() is an action which represents

observ-

ing physical objects within an observation radius

(

). If

located in

PhA ∈ PA

is 1, then

U can observe the status of PhA, i.e., U can read

PhA.ae and PhA.rs, and r.state for each resource

r ∈ PhA.rs

. In general, if

of U is

, then U

can observe the status of all areas reachable via at

most

hops in

. For implementation purposes,

Observe() returns the set of resources which U can

observe depending on its O

•

While the

Move

and

Observe

actions can help

locate resource on its own, it can also in-

teract with the cyber algorithm. We assume

that U can use the action Send request() to re-

quest the cyber-subsystem for a resource. When

the cyber-subsystem has located the resource, U

uses Receive(

path

) to receive a

path

from the

cyber-subsystem. Note that although the cyber-

subsystem uses the edges in

to communicate

and locate resources, the

path

delivered to the user

is a path in the graph

from the current location

of U to a location of the resource.

•

The action Acquire(rs) represents the attempt by U

to physically acquire a resource rs which results in

rs.state being set to busy.

•

Release(rs) is used to physically release a resource

rs which results in rs.state being set to free.

4 MUTUAL EXCLUSION IN A

CPS

In this section, we present mutual exclusion algorithms

for a CPS. Each algorithm has two components: (a)

the behavior of active entities describing their efforts

to locate resources and (b) a cyber algorithm.

4.1 Behavior of Active Entities

Behavior describes the steps followed by an active

entity to locate a resource with the help of Observe

MUTUAL EXCLUSION IN CYBER-PHYSICAL SYSTEMS

and Move actions. We consider the following possible

behaviors:

Behavior B

In this behavior, U searches for a re-

source without any help from the cyber-subsystem. At

each step, if U observes a free resource, it will attempt

to acquire it. If unsuccessful (note that another active

entity may attempt to acquire the same resource at

the same time), then it picks a random adjacent area

and moves to that area via the connecting reachability

edge.

Behavior B

This behavior represents the other ex-

treme wherein U sends a request message to the cyber-

subsystem and waits for a response; then it follows

the path received in the message. In this case, it will

always successfully acquire a resource in the target

area as the access is regulated solely by the cyber-

subsystem.

Behavior B

In this behavior, U sends a request mes-

sage to the cyber-subsystem and waits for a response.

Subsequently, it follows the path received in the mes-

sage. However, as it moves, it also observes each

intermediate PhA for a free resource; if available, it

will attempt to acquire it.

Behavior B

, after delivering a path to a re-

source

to U, the cyber-subsystem may ﬁnd that

another resource

has been released subsequently

which may be closer to U.

is a variation of

wherein U can dynamically accept updated paths from

the cyber-subsystem while it is moving, and follows

these shorter paths.

We have identiﬁed some possible behaviors of ac-

tive entities above. Clearly, variations of these behav-

iors (including more complex ones which, for instance,

involve active entities cooperating to avoid conﬂicts)

can be deﬁned in our proposed model. We have iden-

tiﬁed and studied one such cooperative behavior and

has shown that it can signiﬁcantly reduce the time to

acquire a resource (Gujrati and Singh, 2011).

4.2 Cyber Algorithms

To accommodate the different behaviors (

, and

), we have developed both centralized and dis-

tributed cyber algorithms. The algorithms assume that

each

∈ CE

runs exactly one process denoted by

each physical area

PhA

is sensed by exactly one cyber

entity

and sensing ranges of cyber entities do not

overlap. This eliminates possibilities of two cyber enti-

ties sensing the same resource and a physical resource

not being sensed by any cyber entity. Due to space

limitations, we do not describe centralized algorithm

and certain details such as how cyber-subsystem re-

acts when a resource reserved for a user is acquired by

some other user.

In this paper, we have explored two distributed

strategies to solve mutual exclusion in CPS. The ﬁrst

strategy, termed as KRL CPS, is a variation of the

KRL algorithm wherein we perform edge reversal only

when an active entity moves the resource to another

location. Thus, in the scenario in Figure 2(a), the

remains the sink node as long as there is a resource in

PhA

The second strategy, termed Shortest Path Re-

source Allocation (SPRA), disregards the existing path

information and creates paths on a on-demand basis.

SPRA maintains a set of trees called

SPTree

s. Each

SPTree

is rooted at

where

senses a free resource.

Each

maintains two variables,

ptrR

and

height

attr

is a tuple (

ptrR

, height

). Initially, for all

attr

= (

NULL, ∞

). Each

also maintains a set

Nbr Attr

which contains the most recent

attr

elements received

from the neighboring nodes.

Figure 2(b) shows an initial setup showing two

SPTree

s rooted at

and

. When a process makes a

request, the request is forwarded via the parent pointers

to the tree root. For example, when

located in

PhA

makes a request,

will propagate the request to

On receiving this request,

sets

R1.state

to locked

and sends conﬁrmation back to

via intermediate

child pointers. When

receives the conﬁrmation, it

has to move along the path to reach

PhA

SPTree

Algorithm 1: SPTree management.

update attr

in Nbr Attr

;

if (ptrR

= SELF or ptrR

= P

)

/* V

either senses at least one free resource

or P

points to P

itself. */

exit();

else

min height ← min(height

), attr

∈ Nbr Attr

;

if (height

≤ min height + 1)

/*height

is already minimum.*/

exit();

else

attr

← (P

, height

+ 1);

broadcast attr

;

are created and maintained as follows. As soon as

senses a free resource, it sets

attr

to (

SELF, 0

). When-

ever

attr

changes,

broadcasts the new value to its

neighbors. If

is neighbor of

, on receiving

attr

executes Algorithm 1 which ﬁrst updates

Nbr Attr

and then updates

attr

if the value received from

provides a lower cost path to a free resource. When a

resource, say

PhA

in Figure 2(b) is locked,

changes

attr

to (

NULL, ∞

), and sends this value to

its children (which are propagated further). Hence, all

SENSORNETS 2012 - International Conference on Sensor Networks

1 2 3

4 5 6

7 8 9

R1(free)

R2(free)

(a) KRL initial DAG.

1, S, 0 2, 1, 1 3, 2, 2

4, 1, 1 5, 6, 2 6, 9, 1

7, 4, 2 8, 9, 1 9, S, 0

R1(free)

R2(free)

(b) SPRA initial setup.

1, N, ∞

2, N, ∞ 3, N, ∞

4, N, ∞ 5, 6, 2 6, 9, 1

7, N, ∞ 8, 9, 1 9, S, 0

R1(locked)

R2(free)

1, N, ∞ 2, N, ∞ 3, N, ∞

4, 5, 3 5, 6, 2 6, 9, 1

7, 8, 2 8, 9, 1 9, S, 0

(busy)

(free)

(d)

discovers new path.

1, 2, 2 2, 3, 1 3, S, 0

4, 5, 3 5, 6, 2 6, 9, 1

7, 8, 2 8, 9, 1 9, S, 0

R1(free)

(free)

(e) U1 releases R1.

Figure 2: (a):

KRL

Algorithm, (b) to (d):

SPRA

Algorithm -

S = SELF

N = NULL

, triple at each node = (

ptrR

height

the nodes in the tree will set their

attr

to (

NULL, ∞

)

(shown in Figure 2(c)). Subsequently, these nodes

connect to trees on a on-demand basis. For example,

when

receives a request from

will attempt to

rediscover a resource. It initiates a breadth ﬁrst search.

The resulting

SPTree

s are shown in Figure 2(d). Fig-

ure 2(e) shows

SPTree

s after

moves

PhA

and releases it there.

5 SIMULATION AND RESULTS

We used the OMNeT++ Discrete Event Simulation

System (Varga, 2001) to simulate the algorithms.

MiXiM (Wessel et al., 2009), an extension of OM-

NeT++ to simulate wireless and mobile networks, pro-

vides detailed models of the lower layers of the pro-

tocol stack. Our simulation is built on top of MiXiM.

See (Gujrati and Singh, 2011) for detailed discussion

on node architecture in the simulation.

In the following discussion, active entity and re-

source will be referred to as person and wheelchair

respectively. We use AT to represent the Acquire Time,

which is the time elapsed from when a request is made

and a wheelchair is acquired, NM represents the to-

tal number of messages generated in the network per

request, and NH represents the number of physical

areas a person needs to move to get a wheelchair. AT,

NM and NH are averaged for 100 requests per per-

son. For the experiments, we ﬁxed the time it takes

for a person to move from one area to an adjacent one

to 3 seconds, and assumed that each person uses a

wheelchair for a random amount of time between 20

and 30 seconds. Furthermore, we assume that cyber

entities sense the status of the physical area it is lo-

cated in every 100ms, and the default

is 1. We use

the

-tuple

< M, K, B

, N

to represent a system

conﬁguration having

persons and

wheelchairs

located in a grid of size

M ∗ K

(or

M∗K

) of physical

areas and all

persons following behavior

x,y

represent the cyber entity located in row

and column

y of the grid.

• Comparison of KRL CPS and SPRA.

In the ﬁrst scenario of KRL CPS, which we call KRL-S,

a wheelchair is released at the same location where

it was acquired. KRL-D refers to a scenario in which

wheelchair is released at a random location (which

is more realistic). As shown in Figure 3, for conﬁg-

uration

< 8, 8, B

, 6, 3 >

, NH is 18.3 in KRL-D, and

12.4 in KRL-S. The difference is due to the fact that

when the wheelchair moves from its original location,

the edges are reversed (hence, a linear chain of parent

pointers will be created from its original location to

the new location). The corresponding

for SPRA

is 8.3 with wheelchairs released at random locations.

As can be seen in Figure 3, as the

is increased

(with

kept constant), the difference between the

performances of the three algorithms reduce. This is

due to the fact that with more wheelchairs (e.g., 10

wheelchairs in a

8∗8

), the trees have smaller depths.

As NH is higher for KRL CPS as compared to SPRA

algorithm, one would expect AT also to be higher. Fig-

ure 4 shows the performance of these algorithms with

respect to AT. As can be seen, SPRA outperforms both

KRL-D and KRL-S. We also simulated similar conﬁgu-

rations with

12∗12

and the results follow a similar pat-

tern. However, the performance gain for SPRA comes

at the expense of increased number of messages. To re-

create paths on demand, we have to conduct a breadth

ﬁrst search when a wheelchair is requested. Whereas

NM is 31 for KRL-S and 47 for KRL-D, it is 93 for

SPRA for conﬁguration

< 8, 8, B

, 6, 3 >

. However, as

is increased (keeping

ﬁxed), we ﬁnd that the

cost of re-creating paths drops as it is more likely that

nearby resources can be found (and hence, the breadth

ﬁrst search terminates in relatively fewer number of

hops). Our simulation show that

drops from 93 to

61 as N

is increased from 3 to 6.

KRL-D

KRL-S

SPRA

Figure 3: NH vs N

for < 8, 8, B

, 6, N

>, 3 ≤ N

≤ 10.

MUTUAL EXCLUSION IN CYBER-PHYSICAL SYSTEMS

100

110

120

AT (sec)

KRL-D

KRL-S

SPRA

Figure 4: AT vs N

for < 8, 8, B

, N

, 3 >, 3 ≤ N

≤ 7.

• Comparison of Different Behaviors.

Next, we wanted to analyze the impact of different

behaviors of active entities on AT and

. In what

follows, SPRA-N denotes SPRA algorithm for behav-

ior

where

1 ≤ N ≤ 3

. We ﬁrst studied the impact

of releasing wheelchairs in random areas on

and

by keeping

constant and varying

. The re-

sults are shown in Figure 5. As discussed earlier, in

(referred to as NoCS in Figure 5(a)), a person attempts

to visit areas on its own (without help of the cyber-

subsystem). This results in a high value of AT. For

the other three behaviors, we observed the following:

When

is 7 and

is 3, there is increased competi-

tion for wheelchairs. As a result, it is less likely that a

person will locate another free wheelchair when it is

moving to the location of the free wheelchair initially

identiﬁed by the cyber-subsystem (which it tries to

do in

and

). Similarly, it is less likely that the

cyber-subsystem will be able to provide an updated

path. Hence, the performance of the three behaviors

coincide for this scenario. As the number of persons is

decreased (from 7 to 5), there is less competition and

the scenarios wherein free wheelchairs can be located

by the person or the cyber-subsystem become more

probable, and SPRA-3 outperforms SPRA-2, which in

turn outperforms SPRA-1. As

is further decreased

(say to 2), we ﬁnd that a free resource will always be

available and hence, the initial location identiﬁed by

the cyber- subsystem is most likely to be the nearest

one. Hence, the performances again converge. The

impact on NH is similar (see Figure 5(b)).

• Impact of O

In this setup, we increased

of each person from 1

to 8 for conﬁgurations

< 8, 8, B

, 5, 3 >

1 ≤ i ≤ 3

. The

results for SPRA are shown in Figure 6. The perfor-

mance of

is not impacted by

. The performance

improves as

is increased from 1 to 4 – this is

due to the fact that a person can observe more areas and

hence the chances of ﬁnding a nearby free wheelchairs

increase. However, as

is increased further, perfor-

mances of

starts degrading because the observation

zones of the users overlap a lot. Hence, there are

more chances that whenever a wheelchair becomes

free, multiple users might observe it and deviate from

105

115

AT (sec)

NoCS

SPRA-1

SPRA-2

SPRA-3

(a) AT vs N

NoCS

SPRA-1

SPRA-2

SPRA-3

(b) NH vs N

Figure 5: Impact of varying

and

when

= 3

for G

8∗8

AT (sec)

SPRA-1

SPRA-2

SPRA-3

Figure 6: Impact of increasing O

on AT .

their original paths towards this free wheelchair. Since

only one of them will be successful, others will have to

incur additional hops. The performance of

show a

similar pattern except that when

is increased from

1 to 4, we do not see much change. In this case, we

ﬁnd that the cyber-subsystem is able to provide quick

updates of newly freed wheelchairs which are close.

6 CONCLUSIONS AND FUTURE

WORK

Graph based models with various assumptions related

to message transmission and processing times have

provided a strong foundation to study distributed algo-

rithms in a TDS. This paper provides a step towards

studying similar algorithms for CPSs. We presented a

graph based formalism to model both the cyber- and

the physical-subsystems and the interactions between

them. Based on this model, we presented algorithms

SENSORNETS 2012 - International Conference on Sensor Networks

for the mutual exclusion problem. Each algorithm had

two components, one describing the behavior of users

in the physical-subsystem and the other describing the

cyber algorithm. We identiﬁed several characteristic

of a CPS which make solutions for TDS inapplicable

to a CPS. We simulated all the presented algorithms

using OMNeT++. The results provide suggestions on

the best algorithm to use in different scenarios. For

example, the results show that when fewer resources

are present, it might be best to rely completely on

the cyber-subsystem; otherwise, participation of users

in locating resource can improve performance. The

model proposed in this paper opens the possibility of

studying more complex scenarios and algorithms for

CPSs. These possibilities include associating proper-

ties with the reachability edges in

and cooperation

between the users in locating resources. Finally, in the

SPRA

algorithm, identifying mechanisms via which

existing tree information could be utilized in creating

on-demand paths to reduce number of messages is a

subject of future research.

ACKNOWLEDGEMENTS

This work was supported in part by NSF Grant

0615337 and K-State Targeted Excellence program.

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