Optimization and Scheduling of Queueing Systems for Communication

Systems: OR Needs and Challenges

Attahiru Sule Alfa

1,2

and B. T. Maharaj

Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa

Keywords:

Optimization, Scheduling, Queueing, Congestion Control, Network Performance, Cognitive Radio Networks,

Wireless Sensor Networks, Internet of Things.

Abstract:

The modern communication system is growing at an alarming rate with fast growth of new technologies to

meet current and future demands. While the development of devices and technologies to improve and meet the

expected communication demands keeps growing, the tools for their effective and efﬁcient implementations

seem to be lagging behind. On one hand there is a tremendous development and continued advancement of

techniques in Operations Research (OR). However it is surprising how the key tools for efﬁciently optimizing

the use of the modern technologies is lagging behind partly because there isn’t sufﬁcient cooperation between

core OR researchers and communication researchers. In this position paper, using one speciﬁc example, we

identify the need to develop more efﬁcient and effective OR tools for combined queueing and optimization

tools for modern communication systems. OR scientists tend to focus more on either the analysis of commu-

nication issues using queueing theory tools or the optimization of resource allocations but the combination of

the tools in research have not received as much attention. Our position is that this is one of major areas in the

OR ﬁeld that would beneﬁt communication systems. We brieﬂy touch on other examples also.

1 INTRODUCTION

The demand for communication systems keeps grow-

ing on an ongoing basis. Communication industry

researchers are continuously working at coming up

with new technologies for meeting the demands. In

a recent ACG Research report (ACG, 2015) it was

pointed out that for an area of 1,200 square kilome-

ter metro area having approximately a population of

about 2.5 million people the bandwidth requirement

for backhaul at a cell site could be as high as 2.5

Gbps in the year 2018 and about 10 Gbps of Ether-

net links and 10 Gbps rings to meet the demand re-

quirements and support the expected growth. Part of

these growths in demand have to do with the shifts

in customers to data. In the past media and video

was less than 10% of the trafﬁc and now it is almost

50% according to the recent Global telecommunica-

tions study: navigating the road to 2020 (EYReport,

2015). Bandwidth available is limited however efforts

are been made to squeeze more from what is avail-

able and also to release some inefﬁciently utilized ra-

dio frequencies for other uses. Hence telecommuni-

cation engineers do not only have to ensure that they

could provide the capacity for these demand growths

but make sure also that the capacity is efﬁciently well

managed.

In trying to provide efﬁcient and effective com-

munication services for the future we need to harness

several key tools mostly OR based. Our position is

that this has not received the proper attention it de-

serves from the OR researchers and practitioners. The

aim of this paper is to try, with the aid of some ex-

amples, to identify the major role that OR researchers

can play in planning modern communication systems.

Historically queueing model by itself has been ex-

tensively used in analyzing the performance of com-

munication systems. In fact to the extent that when

people talk of performance analysis in communica-

tion systems they are most likely referring to queue-

ing model analysis of a communication system. Of-

ten the model is for a particular protocol. A protocol,

in simple terms, is the rule by which a system oper-

ates. When the protocol for a system changes, the

queueing system that represents it changes and hence

the system would need to be re-modelled in order to

obtain its performance. Keeping in mind that a com-

munication system designer may have a plethora of

430

Sule Alfa A. and Maharaj B.

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges.

DOI: 10.5220/0006235504300439

In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems (ICORES 2017), pages 430-439

ISBN: 978-989-758-218-9

possible protocol designs for a particular system, de-

ciding on the ”best” design becomes an exercise of

modelling and evaluating the system with each pro-

tocol and evaluating it. This could be a nightmare

of combinatorial problem. The ideal thing would be

to be able to develop a combined queueing and op-

timization model where the parameters of the queue-

ing system are to be decision variables in the opti-

mization problem and a performance measure of the

system is the objective function. This is straightfor-

ward enough. However when we look at the literature

on this subject the research on the topic lags behind

considerably in meeting the challenges of appropriate

mathematical modelling of the modern communica-

tions needs. That is why we have decided to further

bring this to the attention of OR researchers and ana-

lysts.

2 COGNITIVE RADIO

NETWORKS

Cognitive radio networks (CRN) is one of those tech-

nologies that is being pursued as a way to increase

capacity for communication. CRN emerged from the

observations of some researchers and the FCC (Fed-

eral Communications Commission) that some of the

licensed frequencies, especially the TV band, are un-

derutilized. As a result CRN is a network in which

when the primary user (who has license for a partic-

ular channel) is not using it a secondary user may try

and access it provided it does not interfere (beyond

a tolerable limit) with the primary user. For more de-

tails about this technology and associated background

see (Mitola and Maguire, 1999) and (Haykin, 2005).

In CRN a secondary user (SU) senses a channel

and may access it if it is not in use. We call this ac-

cess approach the overlay. However if the channel is

in use by the primary user (PU) the SU may still ac-

cess it if the SU can transmit at a power level that will

not interfere with the PU. This we call the underlay.

The methods for sensing the channels are well docu-

mented in the communication literature.

The question here is when a channel can be ac-

cessed by SUs how does the system decide on which

SU to access which the channel and for how long.

This becomes a major queueing and optimization

problem which is better addressed by using OR tools.

In the next section we show how OR tools can be con-

sidered as tools for this and the challenges involved.

In real life there are several channels involved in

communication systems. However to make it simple

for expositional purposes we consider a single chan-

nel model for CRN. Later we discuss how the multiple

Busy

Idle

Fig 1. Busy and Idle times (single channel)

Time

Figure 1: Busy and Idle times (single channel).

channel cases are studied.

Consider a single communication channel used by

one or several PUs. For simplicity let us assume that

the PUs arrive according to a Bernoulli process with

parameter λ

and the channel can process at geomet-

ric distribution with probability µ. Keep in mind that

the PUs required processing rate could be µ

< µ.

This system can be studied as the Geo/Geo/1 queue.

Even if the arrival and processing processes are not

simple we can still analyze the system using a sin-

gle server queueing model. We chose to work in dis-

crete time because modern communication systems

are digital. Further consider a case on one channel

licensed to a PU which is either busy or idle. We

can represent it as an alternating stochastic process

{busy, idle}. A simple example of that is an alter-

nating Markov renewal. For the sake of explaining

we consider the special case of Markov chain, with

two states {0, 1} where 0 represents busy and 1 rep-

resents idle. Let X

be the state at time n and deﬁne

i, j

= Pr

{

n+1

= j, X

= i

}

, ∀n then we can write the

transition matrix of this system as

P =



0,0

0,1

1,0

1,1



The following diagram (Fig. 1) is a schematic rep-

resentation of idle and busy periods of this channel.

If we now introduce an SU with arrival probability

, this SU may try and access the channel using the

overlay or underlay schemes.

2.1 Overlay Scheme

In the overlay scheme, the SU will only access the

channel when it is idle and has to vacate it when the

PU returns to the channel, i.e. when it becomes busy

again. So in essence an SU sees this channel as a va-

cation queueing system in which the server (channel)

is on vacation when it is busy with the PU. The SU

can thus only be served during the queues idle period

(when the PU is not occupying it). This is a queueing

problem which can be analyzed using standard queue-

ing models. This problem is quite straightforward if

all we have is just one SU trying to access the channel.

The SU just waits for the time it detects the channel

to be idle and then access it. The point in time when

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges

431

Time

Fig 2. Busy and Idle times (multiple channel)

Channel 1

Channel 2

Channel 3

Figure 2: Busy and Idle times (multiple channel).

the channel becomes idle is a point process and the

duration of the idle period is stochastic.

The question that arises then is when we have

more than one SU waiting to access the channel; how

do we allocate the channel to the SUs? What prior-

ity schemes do we use? This calls for an optimiza-

tion tool for scheduling the SUs. Keeping in mind

the stochastic nature of the idle and busy periods of

the channel a system scheduler has to implement an

efﬁcient scheduling procedure. Now if we have mul-

tiple channels, which is more realistic, then we are

dealing with a system of superposition of several of

the channel Markov chains. For simplicity let us as-

sume that the channels are identical with the same

Markov chains with representation P, then the result-

ing Markov chain that represents all the K channels

has Markov chain with transition matrix P

written as

= P ⊗ P ⊗ · ·· ⊗ P,

where there are K Kronecker products of the matrix

P , i.e. P

j=1

P. A good diagrammatic example

of the busy and idle channel behaviours of this can be

demonstrated by the case of K = 3 in Fig. 2.

In this case we need to keep track of which queue

(channel) is idle and which one is busy at all times.

Selecting which channel to assign to which SU is a

challenging dynamic assignment problem; scheduling

when to let a particular SU access a channel is also

a challenging OR problem, especially if we assign a

group of channels to some SUs ((Jiao et al., 2011; Jiao

et al., 2012)).

Finally there are usually some SUs that have high

data transmission rate and often are willing to pay for

superior service. Such SUs require that more than one

channel are assigned to them ((Jiao et al., 2011; Jiao

et al., 2012)). How do we develop an optimization to

handle this type of problem? For example, consider

the case of three identical channels above. If we have

say three SUs, and one of them requires two chan-

nels while the third channel is shared by the other

two, how do we decide which two channels to as-

sign to this special SU? There are three possible ways,

all dependent on the stochastic process describing the

channels. One just has to imagine what happens when

we have N (N >> 1) channels and M (M >> 1) SUs

with the i

SU requiring m

channels. . Even for the

Capacity

Time

Fig 3. Capacity (single channel)

Figure 3: Capacity (single channel).

case when

∑

≤ N it could still be a major combi-

natorial problem, combining queueing and optimiza-

tion.

These are some of the issues that arise in the CRN

technologies, and which we think can beneﬁt tremen-

dously from the OR communities.

2.2 Underlay Scheme

Dealing with the underlay scheme is about the same

as the overlay scheme except that we now have to also

allocate a power level to an SU to ensure that it does

not interfere with a PU transmission. So the addi-

tional question here is what power level should we

assign to an SU and to which SU in order to maxi-

mize communication capacity?

In addition we may also be in a position to have

a hybrid scheme in which some SUs are placed on

overlay scheme, some on underlay scheme and some

on a combination of both. The question is how do

we determine which ones to assign what scheme and

how? This is an optimization problem which also has

impact of the network performance.

Let us ﬁrst look at the case of one channel in

which an SU wants to consider underlay in addition

to overlay, i.e. a hybrid. For the one channel even

though we may know the busy and idle period, during

the idle period we know that an SU can transmit at its

full power (if possible), if it is the only one transmit-

ting. However if it wants to transmit also under the

underlay scheme the power level allowed may vary

depending on what is the level of power of the PU.

We present a schematic diagram of the situation under

full capacity below in Fig. 3, i.e. when the channel is

idle. For the case of underlay,he available capacity

cannot be higher than what is shown in Fig. 3.

If we now consider the case of three channels, su-

perimposed and then capturing the combined capacity

we may have a case like the one below in Fig. 4.

How to now assign the channels and power be-

comes a major queueing, assignment and scheduling

problem which is not as straightforward.

In what follows we introduce a small generic re-

source allocation problem and use that as the basis of

our discussions in comparing the papers in the liter-

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

432

Time

Capacity

Time

Channel 1

Channel 2

Channel 3

Fig 4. Capacity (multiple channels)

Figure 4: Capacity (multiple channel).

ature. Consider a simple CRN problem in which we

have K PU channels. There are M SUs looking for ac-

cess to the PU channels. Each SU, s = 1, 2, ··· , M has

a maximum power source of P

max

. If SU s is allowed

to transmit on channel k with power level P

, then

its capacity, c

will be given as c

= log



1 + γ



where γ

is the noise level associated with SU s trans-

mitting on channel k. This is essentially a simpliﬁed

Shannon’s capacity formula or a formula derived from

it. Whether we are dealing with capacity, throughput

or data rate a version of this formula is what we use.

Let x

= 1 if channel k is assigned to SU, s and

zero, otherwise. Generally the throughput and data

rate resulting from this are directly proportional to

this capacity. So in essence the total capacity assigned

to this SU, s will be

∑

k=1

In RA problem our interest would be to maximize

the total weighted capacity for all the SUs, with the

weight w

assigned to SU s. Hence the objective func-

tion of this generic problem will be

max z =

∑

s=1

∑

k=1

. (1)

This is a non-linear function in P

and x

Next we consider the constraints. The ﬁrst one

is that we want to ensure that at least one channel is

assigned to an SU, on the assumption that M ≤ K. So

we need the constraint

∑

k=1

≥ 1, ∀s = 1, 2, ··· , M, (2)

and also a constraint that ensures that we do not assign

more than a channel to more than one SU, i.e.

∑

s=1

≤ 1, ∀k = 1, 2, ··· , K. (3)

The next constraint is that we cannot allow the

total power generated by an SU to exceed its power

limit. So we need the constraint that

∑

k=1

≤ P

max

, ∀s = 1, 2, ·· · , M. (4)

A key requirement in CRN is that the SU should

not interfere with the PU, or at least the interference

should not exceed the maximum allowed level. This

can be easily captured by requiring that the power

reaching the PU should not exceed a particular value

power

. So the next constraint is

∑

s=1

∑

k=1

≤ P

power.

(5)

with the variables allowed to assume any non-

negative values.

Given that SUs usually have a minimum require-

ment for QoS we assume that there is a constraint in

this regard also. For example, an SU, s, may require

a minimum of σ

of total capacity after combining a

number of sub-channels assigned, so this leads to the

constraint

∑

k=1

≥ σ

, ∀s = 1, 2, ·· · , M. (6)

Finally we have the two critical but common con-

straints, i.e. that of zero-one on x

and non-negativity

on P

, both written as

∈

{

0, 1

}

. (7)

≥ 0. (8)

In summary, Equations (1) to (8) form the re-

source allocation (RA) problem for this simple exam-

ple. As one can see, in its simplest form, the objec-

tive function in non-linear, and constraint (6) is non-

linear. Also one variable, x

is zero-one while P

a simple non-negative variable. So unless there is a

signiﬁcantly different problem studied, non-linearity

and integer variables (zero-one) are unavoidable in

the formulations. That is why in general we have a

non-linear mixed integer programming problem for

RA. The issue now is how it has been handled in the

literature. A more detailed discussion of this can be

found in (Alfa et al., 2016).

It is however important to point out some aspects

of this formulation that could be further improved to

reﬂect an attempt to truly optimize the system as a

whole. We know that the resulting capacity available

to an SU, after the optimization, determines the de-

lay or latency of packet transmission. So we need to

incorporate additional constraints, based on queueing

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges

433

models, that limit the delay or add a delay cost com-

ponent to the objective function. These are usually not

incorporated in the RA models because of the com-

plexity it would introduce to the problem. This is one

major reason why it is important for the communica-

tion system researchers and OR analysts/researchers

need to collaborate on carrying out major complete

model analysis.

SUGGESTED IDEA FOR COLLABORATION:

Telecommunication researchers often resort to the

use of simple heuristics to quickly obtain solutions

to the type of optimization problems discussed

above. The heuristics are usually not rigorously

studied before implementation. For example,

exploring and understanding how “good” the

solutions are is very important especially now that

there is a need to “squeeze” as much as possible

from the network. Solutions that are not proven

to be efﬁcient, for example if the gap between

the solution and the bound is large, could be

misleading. This is where it is very important for

the telecommunication researchers to collaborate

more with OR analysts whose interests, capacity

and experience are in these aspects. The OR

analysts on their own, would probably have more

interests in the mathematical analysis of the

system and looking for bounds. In the process

may assume away some important aspects of the

problem which a telecommunication researcher

knows is very important for the problem. That is

why the two groups need to collaborate and work

together in coming up with better solutions. The

combined collaborative effort of the two groups

would lead to much better solution.

3 WIRELESS SENSOR

NETWORKS AND THE

INTERNET OF THINGS

The Internet of things (IoT), which is probably more

correctly be termed the Internet for Things (IfT) as

suggested by Kevin Ashton, the originator of the term

IoT (Peter Day’s World of Business, 2016 (BBC,

2016)), is seen as one of the technologies that would

drive our daily activities and hence very important.

To quote the Wikipedia,“IoT is the internet working

of physical devices, vehicle, building and other items

embedded with electronics, software, sensors, actu-

ators, and networking connectivity that enable these

objects to collect and exchange data”. It is immedi-

ately clear that one of the technologies that would en-

able the IoT is wireless sensor networks, among many

other technologies. A wireless sensor network (WSN)

is a self-organizing network that consists of a number

of sensor nodes deployed in a certain area. The sen-

sor nodes basically sense and acquire data from the

environment, process data for storage, as well as a

communicate (transmit) the data to a sink node. It

is the communicated data that the IoT system uses

to actuate activities in response thereby generating

device-to-device activities. With the new 5G tech-

nology in discussion it is believed that the IoT will

drive most of actions and activities from smart cities

to smart grid, to smart health, environmental monitor-

ing, infrastructure management, manufacturing, en-

ergy management, city management, home and build-

ing automation, transportation, etc. So ﬁrst we con-

sider the role of OR in sensor networks modelling and

analysis.

3.1 Wireless Sensor Networks

There are a number of different applications of sen-

sor networks in areas such as environmental moni-

toring, industrial control, disaster recovery, and bat-

tleﬁeld surveillance. The major constraint in large

scale deployment of WSNs is the limited capacity of

processing, storage and energy of the wireless sensor

nodes. It is important that the buffer capacity is suf-

ﬁcient to avoid data loss, that the processing capacity

is high enough to obtain very good latency, especially

for time sensitive data for the Internet of Things, and

most important is that processing is limited to times

when the system can be utilised efﬁciently, i.e. en-

ergy is conserved through the sleep/awake manage-

ment of the sensors. In order to effectively carry out

the design of many aspects of sensor networks, a very

good queueing analysis is important. Queueing the-

ory plays a major role than has been emphasized in

the literature.

WSN is a collection of several nodes of sensors

of all types connected via wireless channels of differ-

ent capacities with varying channel conditions. The

sensor nodes are usually of different capacities and

different functionalities. Some of them collect, pro-

cess and transmit data, and others only carry out a

few of the functions. Let us denote by N a set of sen-

sor nodes where N =



and N =

{

, N

, ···N

}

Let A be the set of channels connecting pairs of sen-

sor nodes. For example, let A

i, j

be a connection be-

tween sensor nodes N

and N

, then A is the set of

all those channels. Let C

i, j

be the capacity associ-

ated with channel A

i, j

, and K

as the buffer capacity

and P

as the processing capacity associated with sen-

sor node i. We can therefore say that a WSN can be

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

434

7 15

Sensor node

Fig. 5 Sensor node distribution

Sink node

Figure 5: Sensor node distribution.

described by a network G =



N , A



with attributes



, P

), (C

i, j

), i ∈ N , (i, j) ∈ A



. See Fig. 5 as an

example.

1) Queueing Aspects of WSN: The ﬁrst thing one

notices about WSN is that it is like a network of

queues with each sensor node representing a queue-

ing node. Since data arrival is usually not necessarily

Poisson type, and more often kind of correlated, sim-

ple single node queues or even simple queueing net-

work models such as the Jackson networks are not ap-

propriate for modelling the WSN. In addition, given

that we need to include sleep/awake mode schedul-

ing the model then becomes more complicated. This

calls for more sophisticated and more representative

queueing models, the types that queueing theoreti-

cians do not seem to have focused on yet. Consider-

ing queueing models that assume non-renewal types

of arrivals with bursty instances is more appropriate.

However then including such processes in a queueing

network, which is beyond the Jackson’s model, is a

challenge which queueing theorists need to tackle.

2) Power Management of WSN: Due to the fact

that most sensor nodes are battery operated, i.e. have

limited available power source, it is important to ef-

ﬁciently manage them effectively for a long lasting

network life. Usually a sleep/awake mode is im-

plemented to achieve this goal; a very good vaca-

tion queueing model in which the scheduling of the

sleep/awake mode is well controlled. This involves

a combined queueing model with optimization tech-

niques. Queueing theory can prove to be an effective

tool to analyze and design efﬁcient power allocation

schemes to increase the power efﬁciency of WSNs

(see (Kabiri et al., 2014)). Sleep/awake models are

based on special kinds of vacation models. When

the sensor goes to the sleep mode, that means it is

switched off and cannot process data. This is es-

sentially a vacation model. Data arrivals accumulate

at the buffer. The node wakes up depending on the

time which is based on a policy of how many pack-

ets are waiting (N), how long they have been wait-

ing (T) and the total amount of Kilo-bytes of data

(D). These models are classiﬁed as N-policy, T-policy

or D-policy models. Recently there have been com-

bined versions of these models, such as the NT-policy,

and there are research activities going on regarding

developing ND, and NDT-policies. Sleep/wake-up

schemes essentially makes use of duty cycle schemes

which are used to wake a node up from an idle state

to the busy state by turning on the radio server. This

plays an important role in the level of power sav-

ings in the context of MAC protocols. The authors in

(Kabiri et al., 2014) derived an analytical model utilis-

ing a M/G/1 queue to model the sensor node; and by

altering the queue parameters, different sleep/wake-

up strategies were analysed. Some IEEE 802.11 MAC

protocols like the sensor MAC, sparse topology and

energy management, or the Berkeley MAC utilize a

queued wake-up where a threshold value is used to

control the average time of switching on a node and

the latency for buffered data packets. Determining the

optimal value of the packet queue length of a node af-

ter which the node is switched on for transmission, is

referred to as the N-policy. For more information see

(Jiang et al., 2012).

Let d

be the sum of the delays to data processing

at node N

and transmission from that node, and if

data is generated at node N

at the rate of λ

, then we

have

= d (λ

, P

, K

, T

), ∀i, (9)

and ω

th power consumption at that node, given as

= ω(λ

, P

, K

, T

), ∀i. (10)

Given the appropriate parameters of the system we

can obtain the performance measures, whether we use

single node queueing models or queueing network

models.

3) Routing Aspects of WSN: Each sensor node

needs to send its data (processed or unprocessed) to

a sink node where decisions are taken for the whole

system, especially for the IoT to be implementable.

Apart from the usual link costs associated with net-

works in computing optimal routing paths for WSN

we also need to know the energy level at each node.

This aspect has to be incorporated in the routing algo-

rithm keeping in mind that there is a need to preserve

energy at nodes with low level of it. Hence routing

here considers costs of links and nodes. One other

tool that has been incorporated in routing for WSN

is selection of cluster head node which is responsible

for aggregating data from a group of nodes and then

transmitting to the sink node (see Fig.6). This routing

aspect for WSN is unique and has not received enough

attention from the OR researchers. As the 5G technol-

ogy is rolled out and the IoT developed to work using

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges

435

2 4

14 17

Sensor node

Fig. 6 Sensor node distribution with cluster heads

Cluster head

Sink node

Figure 6: SSensor node distribution with cluster heads.

7 15

Fig. 7 Sensor nodes in a depleting scenario

Sensor node

Dead node

Sink node

Figure 7: Sensor nodes in a depleting scenario.

that technology we want to maximize the technology

to ensure high effectiveness and efﬁciency. This calls

for the use of very effective and well researched OR

tools.

4) Reliability of WSN: The reliability of the WSN

is key to its effectiveness. It is important that if a sen-

sor node is not in operation due to low power or faulty

equipment, that data for the area can still be transmit-

ted. So we need very good reliability model that as-

sesses the impact of dead nodes as shown in Fig. 7.

SUGGESTED IDEA FOR COLLABORATION:

It is important that appropriate queueing models

are developed for WSN in order to obtain more

accurate estimate of delays at the nodes for the

purpose of providing efﬁcient performance. Over-

simpliﬁed and inappropriate queueing models

lead to gross overestimation or underestimation

of performance measures leading to poor power

management and inefﬁcient routing. It is very

common for telecommunication researchers to

assume Poisson arrivals, when often the arrival

process is far from that; and also ignoring corre-

lations in the arrival process is very common in all

the examples discussed in the last few sections. On

the other hand, OR analysts tend to be very rig-

orous by developing general models that are more

appropriate sometimes for unrealistic problems.

Combining the rigour of OR analysts with the re-

alistic view of the problems by telecommunication

researchers would lead to a very appropriate and

effective models. A good collaboration between

the two professions where more realistic models

are developed jointly and the effect of ignoring

some aspects of the systems are well understood

and accounted for would be the direction to go.

3.2 Sensor Node Placements

The placement of sensor nodes in a WSN is another

major factor in the reliability of WSN and its lifetime.

First in order for the WSN to be able to cover all areas

of interest the selection of the node placements have

to be selected strategically. For example, in (Cardei et

al., 2005) the optimization problem is to maximize the

number of set covers by selecting the optimal sensing

range for each sensor in each set cover while ensuring

each target is monitored by at least one sensor. This

problem is referred to as the Adjustable Range Set

Cover (AR-SC) problem and is initially formulated as

the following integer linear program: Consider N sen-

sor nodes s

, . . ., s

and M targets t

, . . ., t

. Let the

sensor have P sensing ranges r

, r

, . . ., r

with corre-

sponding energy consumption e

, e

, . . ., e

. If E is

the initial sensor energy, and a

ip j

, a binary coefﬁcient

which is 1 if sensor s

with radius r

covers the target

. Further let K be an upper bound for the number

of set covers. Then we have the following decision

variables:

Decision Variables:

, boolean variable for k = 1 . . . K, 1 if this subset is

a set cover

ikp

, boolean variable for i = 1 . . . N, k = 1. . . K, p =

1. . . P, 1 if sensor i with range r

is in cover k

The problem can now be set up as an integer linear

program (ILP) as

ILP:

maximize

∑

i=k

, (11)

s.t.

∑

k=1

∑

p=1

ikp

≤ E ∀i = 1 . . . N, (12)

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

436

∑

p=1

ikp

≤ c

∀i = 1 . . . N, k = 1 . . . K, (13)

∑

i=1

∑

p=1

ikp

∗ a

ip j

≥ c

∀k = 1 . . . K, j = 1 . . . M,

(14)

ikp

, c

∈

{

0, 1

}

. (15)

In (Cardei et al., 2005) the integer constraint is re-

laxed to create a linear programming problem which

is then used for the proposed LP based heuristic.

The LP based heuristic uses the values for each vari-

able obtained from solving the LP. The variables with

nonzero values from each cover set are added to the

new set in non-increasing order until all of the targets

are covered. This was improved further by the au-

thors in (Beynon and Alfa, 2015). If a sensor does not

have sufﬁcient energy for the suggested power level

or does not cover any new targets it is not added to

the set. If no more nonzero variables are left for the

current cover and one or more targets remain uncov-

ered then the set is not a cover set. After the maximum

number of cover sets have been attempted to be made

the solution is the set of all valid cover sets.

SUGGESTED IDEA FOR COLLABORATION:

One may argue that this type of problem has been

well studied for years in OR as a class of problem

in the family of maximum covering location

problem. Yet telecommunication researchers still

have unanswered questions about coming up with

very good solutions for the maximum network

lifetime in wireless sensor networks. Perhaps this

is due to some subtleties in the later problem that

are probably ignored in the classical OR versions

of the problem. In our opinion this calls for more

close collaborations between the two groups of

researchers to understand the problem better and

its associated issues.

3.3 IoT

The IoT is essentially driven by the automatic or

“semi-automatic” control system. Data is sent from

some form of sensors, e.g. WSN, and based on the

data an action is taken as seen appropriate. For exam-

ple, a sensor network that is monitoring the temper-

ature at a building keeps gathering data and at each

point may notice that the temperature is too high and

thereby automatically control the system and lowers

the temperature. This is one of the most elemen-

tary ones. Another simple example could be a case

where as soon as a shopper in a grocery store is no-

ticed by a sensor network in the store a message is

sent to the shopper’s home refrigerator sensors which

then sends a message to the shopper’s mobile phone

to let him/her know they need more milk at home.

The communication here is what is called device-to-

device. However more important here is the need for

a process that determines that the milk has reached

low level or expired date etc and request the shopper

to purchase some. This is close to an inventory model

that is automated. The key difference is that there is

a time factor involved. The shopper has to be able to

get the message, from its mobile phone, when they

are still in the store otherwise it is not very helpful.

Hence latency is also a factor.

SUGGESTED IDEA FOR COLLABORATION:

This class of problem is more in the control

domain and requires a good collaboration be-

tween both OR analysts and telecommunication

researchers. It is still an evolving problem which

can beneﬁt early from the collaborations.

In the next section we give a brief example of an-

other type of OR challenges for the future communi-

cation systems.

4 CONNECTING OPTIMIZATION

OF CRN AND QUEUEING OF

WSN

Currently WSN is operated on what is called the un-

licensed channels. These channels are getting con-

gested and it is being proposed that the licensed chan-

nels, which belong to PUs be used for transmitting

data in WSN. The sensor nodes are like queueing

nodes. Data is stored in the buffer and then transmit-

ted when possible. The transmission will be carried

out on licensed channels.

So here is the situation. Considering the PU chan-

nels, the SU, in this case the sensor node(s) will be

assigned a capacity c

on channel k from the opti-

mization model for CRN in Section III. However, be-

cause the assigned capacity and the number of allo-

cated channels are used by the SU to transmit the date

the latency depends on this which should actually be

incorporated as part of the optimization scheme in the

CRN problem. How to capture this feedback is a ma-

jor challenge. Here we present a possible example

method for dealing with it.

Let M be the number of sensor nodes in the WSN,

by trying to combine the two aspects then our Eq(1)

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges

437

in Section III will be

max z =

∑

s=1

∑

k=1

− f (d

) − g(ω

)

, (16)

where f (d

) is the cost of delay at sensor node s and

g(ω

) is the cost of power consumption at node s.

We will also have Eq(9) and Eq(10) as additional

constraints for the optimization problem, in addition

to stability sets of equations.

SUGGESTED IDEA FOR COLLABORATION:

This will be a new and a bit more complex class of

problems. If we decide to include the placement

problem with this then the whole model becomes

very challenging. The question of how to manage

the problem should be of interest to OR analysts

who traditionally have the expertise to handle

them.

We suggest more close collaborations between OR

analysts and Communication network researchers.

5 CONCLUSIONS & THE

POSITION

We start by discussing the ﬁrst example of cognitive

radio networks. Given the information about channel

capacity, which is usually stochastic, for SUs there are

several research results for allocating that resource to

the SUs using optimization tools. However, the allo-

cations provide the service capacity to the users and

hence a very good queueing model is needed to ob-

tain the performance analysis, which itself will now

feed back into the optimization tools. Hence what we

need is a combined queueing and optimization model

in order to efﬁciently model these systems.

Next we consider the wireless sensor networks,

we see that the optimal placement of the sensor nodes

determine network life, its reliability and routing

which affects latency. The placements, routing and

sleep/awake mode determines the queueing delays at

the nodes which need to be included in the optimiza-

tion component of the placements, etc. Hence for the

WSN, combined optimization and queueing models

are essential in order to have a well design WSN.

Finally, keeping in mind that an effective opera-

tion of IoT depends on accurately gathering informa-

tion and passing it to the right destination within a

very short time it is imperative that a combination of

optimization and queueing models are needed for the

planning.

In summary OR analysts and communication

modelling researchers need to try and work very

closely together in order to come up with efﬁcient

tools for analyzing modern day communication sys-

tems. That is the position that we are taking in this

paper.

ACKNOWLEDGEMENT

The authors would like to thank the Advanced Sensor

Networks (ASN) South African Research Chairs Ini-

tiative (SARChI) for their ﬁnancial support in making

this work possible. Thanks to Babatunde Awoyemi

for assisting with drawing the diagrams and to Dr.

Haitham AbuGhazaleh for assisting in recovering the

Latex ﬁle.

REFERENCES

Mitola, J. and Maguire, Jr., G. Q.(1999), Cognitive radio:

Making software radio more personal, IEEE Pers.

Communications, vol. 6, No. 4, Aug. 1999, 13-18.

Haykin, S. (2005), Cognitive radio: Brain-empowered

wireless communications, IEEE Journal of Selected

Areas of Communications, vol. 23, No. 2, Feb. 2005.

Jiao, L. Li, F.Y. and Pla, V. (2012), Modelling and per-

formance analysis of channel assembling in multi-

channel cognitive radio networks with spectrum adap-

tation, IEEE Trans. Vehicular Technology, 61 (6),

2686-2697.

Jiao, L. Li, F.Y. and Pla, V. (2011), Dynamic channel ag-

gregation strategies in cognitive radio networks with

spectrum adaptation, IEEE Globecom 2011, 1-6.

Alfa, A. S., Maharaj, B. T., Lall, S., and Pal, S. (2016),

Mixed-Integer programming based techniques for re-

source allocation in underlay cognitive radio net-

works: A survey, Journal of Communications and

Networks, vol. 18, No. 5, October 2016, 744-761.

Peter Day’s World of Business, BBC World Service, OC-

TOBER 4, 2016.

Beynon, V. and Alfa, A. S. (2015), An improved algo-

rithm for ﬁnding the maximum number of set covers

for wireless sensor networks, Africon, 2015.

Cardei, M., Wu, J., Lu, M. and Pervaiz, M. O. (2005), Max-

imum network lifetime in wireless sensor networks

with adjustable sensing ranges, IEEE International

Conference on Wireless and Mobile Computing, Net-

working and Communications, WiMob 2005 vol. 3,

pp. 438-445, 2005.

Kabiri, C., Zepernick, H. and Tran, H. (2014), On

Power Consumption of Wireless Sensor Nodes with

Min(N,T) Policy in Spectrum Sharing Systems, Pro-

ceedings IEEE Vehicular Technology Conference,

Spring 2014, 1-5.

ICORES 2017 - 6th International Conference on Operations Research and Enterprise Systems

438

Jiang, F., Huang, D., Yang, C. and Leu. F. (2012) Lifetime

elongation for wireless sensor network using queue-

based approaches, The Journal of Supercomputing,

vol. 59, no. 3, 1312-1335.

Forecasting of Mobile Broadband Bandwidth Require-

ments, ACG Research 2015, www.acgcc.com.

Global telecommunications study: navigating the road to

2020, 2015 report EY Building a better working

World.

Optimization and Scheduling of Queueing Systems for Communication Systems: OR Needs and Challenges

439