# Performance Evaluation of Uplink Delay-Tolerant Packet Service in IEEE 802.16-Based Networks

- Zsolt Saffer
^{1}Email author, - Sergey Andreev
^{2}and - Yevgeni Koucheryavy
^{2}

**2011**:549492

**DOI: **10.1155/2011/549492

© Zsolt Saffer et al. 2011

**Received: **15 November 2010

**Accepted: **11 February 2011

**Published: **13 March 2011

## Abstract

We provide an analytical model for efficient dynamic capacity allocation in IEEE 802.16 wireless metropolitan area network, where the nonreal-time traffic can utilize the bandwidth unused by the real-time traffic. We investigate the uplink delay of the nrtPS service flow as a function of the capacity allocations for the rtPS (ertPS) and UGS service flows. Unicast polling is applied for the bandwidth reservation of the nrtPS and rtPS (ertPS) packets. Our analysis accounts for both reservation and scheduling delay components. The nrtPS packets arrive according to Poisson process. The model enables asymmetric capacity allocation, as well as asymmetric nrtPS traffic arrival flows. The analytical model is applied for investigating the influence of the real-time traffic on the delay of the nrtPS service flow. We discuss also the determination of several traffic parameters under different constraints, which have potential applications in network control.

## 1. Introduction

IEEE 802.16 standards family defines an air interface for Broadband Wireless Access (BWA) system. As the result of a recent revision, the contemporary core standard IEEE 802.16-2009 [1] consolidates the IEEE 802.16-2004 standard with several amendments. According to [2], this wireless interface is recommended for Wireless Metropolitan Area Networks (WMANs). The high-speed air interface specified by the IEEE 802.16 standards family enables multimedia services and provides support for several traffic types to ensure the wide range of Quality-of-Service (QoS) requirements of end users.

The standardization of metropolitan-scale wireless access is an ongoing activity performed by the IEEE 802.16 Working Group for BWA with the support of WiMAX Forum [3]. The uplink data packet scheduler, which is out of scope of the IEEE 802.16-2009 standard, has a major impact on ensuring QoS requirements of the end users. As a consequence, numerous research papers deal with the problem of scheduling, like [4–6], in which various frameworks are built and analyzed to guarantee a specified level of QoS. For instance, the work in [7] proposed an efficient QoS architecture, based on priority scheduling and dynamic bandwidth allocation. In [8], authors compare and contrast the performance of various reservation schemes in the framework of the simplified model. For a good summary on QoS in the context of IEEE 802.16, we refer to the online paper [9].

The majority of the analytical works in the literature do not account for both the reservation and the scheduling components of the delay. The importance of accounting for both components to evaluate the overall delay of access-control systems was emphasized by an early fundamental theoretical work by Rubin [10], as well as by our previous papers [11, 12]. For a more practical approach, we refer to [13], in which the realistic performance measures of IEEE 802.16 system are considered by various techniques. In [13, 14], the overall system delay is approximated and verified. In our previous work [15], we established an analytical model for the exact overall delay of the nrtPS service flow with unicast polling in the IEEE 802.16 system. Other polling techniques were studied in [16].

In this paper, we continue the works in [14, 15, 17] by extending the analytical model to perform an efficient dynamic capacity allocation, in which the nonreal-time (delay-tolerant) traffic of each Subscriber Station (SS) can utilize a portion of the spare bandwidth remaining after the capacity allocation for the real-time (delay-critical) traffic flows at every SS. Thus, the model incorporates the effect of the capacity allocation for the real-time polling service (rtPS), extended real-time polling service (ertPS), and unsolicited grant service (UGS) flows on the overall delay of the non real-time polling service (nrtPS) flow. The variable nrtPS capacity of the individual SS is allowed to depend on real-time capacities of every SS. The nrtPS capacity of each SS is determined by means of priorities among them for their non real-time traffic flows. This prioritization allows the realization of different service levels—probably for different prices—in terms of capacity utilization for non real-time traffic. This ensures a guaranteed portion of the total available nrtPS capacity for each SS also in the case when non real-time traffic is saturated at one or more other SSs. The analytical approach leads to a queueing model with batch packet service. The expression for the mean packet delay is given in terms of model probabilities, which are computed from the equilibrium distribution of a properly identified embedded Markov chain.

The analytical model is applied to the performance evaluation of the uplink nrtPS traffic in the IEEE 802.16-based network. Beside providing numerical examples, we study the modeled influence of the real-time traffic on the delay of the nrtPS service flow. We discuss how to take into account an upper bound on mean delay of the nrtPS service flow at the SSs in determining the maximum of the sum of the real-time capacities at every SS. Finally, we introduce a cost model, which takes into account the QoS on delay constraint and on the real-time capacity parameters. The different aspects of this performance analysis have potential applications in network control, since they facilitate the setting of the capacity parameters to the requirements of the actual application scenario.

The rest of the paper is structured as follows. Section 2 gives a brief summary of the channel allocation schemes in IEEE 802.16. In Section 3, we provide the analytical model including the details of the capacity allocation and the uplink scheduling. The analysis of the queueing model follows in Section 4. We determine the mean overall packet delay of the nrtPS service flow in Section 5. In Section 6, we give numerical examples for the performance analysis. Finally the conclusion in Section 7 closes the paper.

## 2. Channel Allocation Schemes in IEEE 802.16

The current IEEE 802.16-2009 standard, as well as its future version IEEE 802.16 m [18], specifies Orthogonal Frequency-Division Multiple Access (OFDMA) at the physical layer.

## 3. Analytical Model and Notations

### 3.1. Restrictions of the Model

- (R.1)
The operational mode is PMP, and TDD/TDMA channel allocation scheme is used. Our TDD/TDMA model derived in this paper can be applied for both OFDMA-based versions (IEEE 802.16-2009 and IEEE 802.16 m).

- (R.2)
Only the uplink traffic is considered, as well as unicast polling is used for nrtPS, rtPS, and ertPS services.

- (R.3)
The uplink packet scheduler at the BS keeps an individual buffer for each SS to serve the nrtPS packets.

- (R.4)
The BE traffic is assumed to be saturated.

- (R.5)
Piggybacking is not used.

### 3.2. General Model

There are SSs and 1 BS in the system, which together comprise stations. Each SS maintains separate buffers of infinite capacity for the uplink packets of different service flows. The nrtPS packets arrive at SS according to the Poisson arrival process with arrival rate for . Hence, the overall nrtPS packet arrival rate is . We call the nrtPS packets arriving to SS as -packets.

The arrival processes at the different SSs are mutually independent. The packet length is fixed and equals bit, which includes data information and the header with packing/fragmentation overhead. The transmission rate of each channel is bps. Therefore, the transmission time of a data packet is . All time durations are measured in seconds.

The duration of the DL and the UL sub-frames are and , respectively. stands for the duration of the reservation interval, and is the maximum available duration of the uplink data transmission in a frame. Therefore, is given by .

The transmission time of a BW-Req is . Hence, and can be expressed as .

### 3.3. Capacity Allocation

Expression (4) shows that the capacity available for the nrtPS traffic is given by an upper-limited discrete-time random variable, whose value is at least one. This ensures that the nrtPS traffic can not be blocked by the UGS, rtPS, and ertPS traffic flows.

Summarizing, our general capacity allocation scheme enables asymmetric capacity allocation for the UGS, rtPS, and ertPS services, as well as asymmetric nrtPS traffic flows.

### 3.4. Model Assumptions

- (A.1)Using (5), (6), (3), and (2) implies that the following relation holds for the arrival rate of each SS below the stability boundary:(7)
This relation ensures the stability of the model.

- (A.2)
The BS uplink scheduler processing delay is negligible.

- (A.3)
The channel propagation time is negligible.

- (A.4)
The transmission channels are error free.

### 3.5. Uplink Scheduling

A BW-Req sent by the SS represents the aggregated request for all nrtPS packets, which are accumulated in its outgoing buffer during the last cycle, that is, since the previous BW-Req sending. We leave the process of bandwidth requesting for rtPS and ertPS packets out of scope of this paper. Furthermore, we assume that the BS knows the number of rtPS and ertPS packets at each SS in every frame and thus it can take them into account calculating the actual available capacity for the nrtPS packets . We note that the actual uplink transmission requirements represented by the rtPS and ertPS requests are always granted, since they are below the available capacity.

*-polling slot*stands for the th polling slot within the reservation interval of the frame, in which the group of SS is polled. At the end of the -polling slot, the BS immediately processes the requests for the nrtPS packets from SS , if any, and serves the individual BS grant buffer of SS . We refer to the end of the -polling slot as

*-reservation epoch*. The BS grant buffer of SS is also served at the epochs following an

*-reservation epoch*by time. Hence, all these epochs, including also the

*-reservation epochs*, are called

*-scheduling epochs*. The positions of the considered epochs are marked in Figure 6.

Receiving a request for the nrtPS packets from SS
at an
*-reservation epoch*, an individual BS grant is assigned to each nrtPS data packet of that request, and then these BS grants are placed into the corresponding individual BS grant buffer of SS
according to their order in the request. Let the number of the BS grants in the buffer of SS
be
. During the service of the individual BS grant buffer of SS
at an
*-scheduling epoch*, the BS takes the available BS grants from that buffer up to the available capacity for the nrtPS service flow of SS
(
) and schedules them for transmission in the UL-MAP of the following frame. Their number equals the number of
-packets transmitted in the next frame,
.

The features of the considered uplink scheduling process can be summarized as follows.

(F.1) The capacity requirements of the UGS, rtPS, and ertPS service flows are always satisfied.

(F.2) The capacity allocation enables priorities for the nrtPS service flows ( at SS for ). This corresponds to a weighted round-robin scheduling of the dynamically variable capacity, which remains available after ensuring the service of the real-time traffic flows.

(F.3)The scheduling mechanism ensures efficient capacity utilization, since the remaining capacity not used by the nrtPS traffic flow at each SS is filled the BE traffic at this SS.

## 4. Queueing System Analysis

The individual polling slot for each SS in a polling cycle and the independent uplink scheduling for the individual SSs together imply that the statistical behavior of the BS grant buffer of a particular SS is independent from the behavior of those of the other SSs. Therefore, we model the stochastic behavior of the BS grant buffer of a particular SS by an individual queueing system.

In this queueing system, the BS grants arrive to the BS grant buffer of SS
at
*-reservation epochs* and they are served at
*-scheduling epochs*.

### 4.1. The Contents of the BS Grant Buffer at -Reservation Epochs

Let
be the number of BS grants in the BS grant buffer of SS
at the
th
*-reservation epoch* for
. The sequence
is an embedded Markov chain on the state space
. Let
denote the probability of transition from state
to state
of the Markov chain, and it is the
th element of the
probability transition matrix
.

Let be the accumulated available capacity for the -packets during consecutive frames for . The distribution of is given as the -times convolution of the distribution of for . The definition of implies that it takes the value 0 with probability 1. It immediately follows that the minimum and maximum values of are and , respectively.

where stands for the largest value of set .

Let denote the equilibrium probability of the state in the Markov chain, and it is the th element of the probability vector . Furthermore, let be the column vector having all elements equal to one.

To keep the computation tractable, an upper limit is set on the states, which results in the finite number of unknowns and equations in the system of linear equations. An appropriate value of depends on the required precision level, at which the probabilities for can be neglected. These probabilities, for , are set to 0.

### 4.2. The Contents of the BS Grant Buffer at -Scheduling Epochs

Let
denote the probability that the number of BS grants in the BS grant buffer of SS
at an arbitrarily chosen
*-scheduling epoch* is exactly
, and it is the
th element of the
probability vector
for
. The probability that an arbitrarily-chosen
*-scheduling epoch* is the
th after the last
*-reservation epoch* is
for
. Note that by definition the 0th
*-scheduling epoch* after the last
*-reservation epoch* is that
*-reservation epoch*.

*-reservation event*. Similarly, by definition the instants of scheduling the BS grants in the BS grant buffer of SS are the

*-scheduling events*. The positioning of the

*-reservation epoch*and the

*-scheduling epochs*(observation epochs) relatively to the

*-reservation*and

*-scheduling events*is shown in Figure 8.

*-scheduling epoch*after the last

*-reservation epoch*, the -packets in the BS grant buffer of SS are those which remained after the last services of the BS grant buffer. Hence, the probability can be established as

### 4.3. The Contents of the BS Grant Buffer at an Arbitrary Epoch

*-scheduling epochs*, the BS grants in the BS grant buffer of SS are those which remained after the service of the BS grant buffer at the last

*-scheduling epoch*. Hence, the probability of being exactly packets in the BS grant buffer of SS at an arbitrary epoch, , is given by

### 4.4. The Size of the Transmitted -Packet Batch

## 5. Overall Delay Analysis

### 5.1. Overall Delay Definition

*overall delay*( ) of the tagged -packet as the time interval spent from its arrival into the outgoing buffer of SS up to the end of its successful transmission in the UL. It is composed of several parts

Here,
is the reservation delay, which is defined as the time interval from the
-packet arrival to SS
until the start of sending a corresponding BW-Req to the BS. We define the *grant time of the tagged*
*-packet* as the
*-scheduling epoch* in the frame preceding the one, in which the tagged
-packet is transmitted.
is the scheduling delay, which is defined as the time interval from the end of sending a BW-Req of the tagged
-packet to its grant time.
is the transmission delay, which is defined as the time interval from the grant time of the tagged
-packet to the start of its successful transmission in the UL sub-frame.

### 5.2. Reservation Delay

*-polling slot*of every polling cycle. Thus, an arriving -packet waits for the reservation opportunity until the end of the current cycle, and, hence, the mean reservation delay is given by

### 5.3. Scheduling Delay

### 5.4. Transmission Delay

### 5.5. Mean Overall Delay

## 6. Performance Evaluation

In this section, we apply the derived analytical model to the performance evaluation of the uplink nrtPS packet service in the IEEE 802.16-2009 network.

### 6.1. Numerical Examples

Here, we provide numerical examples to assess the performance of the IEEE 802.16 uplink nrtPS service flow evaluated with the considered analytical model. In order to generate performance data, a simulation program for IEEE 802.16-2009 MAC was developed. The program is an event-driven simulator that accounts for the discussed restrictions on the considered system model (see Section 3).

In our simulations, we set the default values recommended by WiMAX Forum [3] system evaluation methodology, which are also common values used in practice [21]. We assume a 10 MHz TDD system with 5 ms frame duration, PUSC subchannelization mode, and a DL : UL ratio of 2 : 1. According to [22], the UL sub-frame comprises 175 slots. Assuming MCS of 16 QAM 3/4, the IEEE 802.16-2009 system transmits 16 bytes per UL slot. We consider fixed packet length of 80 bytes (5 slots) for all service flows, which results in having capacity to send 30 packets per UL sub-frame. The remaining 25 UL slots represent the necessary control overhead.

Basic evaluation parameters.

Parameter | Value |
---|---|

PHY layer | OFDMA |

Frame duration ( ) | 5 |

Subchannelization mode | PUSC |

DL/UL ratio | 2 : 1 |

Channel bandwidth | 10 MHz |

MCS | 16 QAM 3/4 |

Packet length | 80 bytes |

Number of SSs ( ) | 6 or 2 |

Total capacity per frame for all SSs | 30 packets |

UGS capacity per frame ( ) | 6 packets |

Minimum (e)rtPS capacity per frame ( ) | 6 packets |

Maximum (e)rtPS capacity per frame ( ) | 18 packets |

Both Figures 9 and 10 show very good accordance between the analytical and the simulation values.

### 6.2. Influence of UGS and (e)rtPS Traffic on nrtPS Delay

In this subsection, we study the influence of the capacity allocation for the UGS and the real-time traffic on the mean packet delay of the nrtPS service flow in the symmetric system for .

### 6.3. Enforcing an Upper Bound on Mean Delay

Our modeling can be also used to enforce specified upper bounds on mean nrtPS packet delays at every SS in a specified range of loads. These bounds can be different for the individual SSs. In this case, the total amount of uplink real-time capacities in the network ( ) is maximized over a restricted parameter set, which is determined by the specified upper bounds on mean nrtPS packet delays and by the specified range of loads. The priority weights of the SSs are assumed to be given.

### 6.4. Cost Model

The minimum can be numerically determined as a function of the load and the real-time capacity parameters at every SS ( and the distribution of for ), by applying the expressions for the mean overall delay of the tagged -packet (22).

## 7. Conclusion

- (i)
the influence of the real-time (UGS and (e)rtPS) capacity allocation on the delay of the delay-tolerant (nrtPS) traffic is captured,

- (ii)
the variable nrtPS capacity of each SS is allowed to depend on the real-time capacities of every SS,

- (iii)
the nrtPS capacity at the SSs are determined by means of priorities among them.

The considered analytical model is verified by means of simulation. This verification shows an excellent accordance between the analytical and the simulation results in a wide range of parameter settings. Hence, our analytical model can be applied to model and analyze the delay of the uplink nrtPS traffic in IEEE 802.16-based network.

- (i)
The dependencies of the mean nrtPS packet delay on the total UGS capacity and on the maximum (e)rtPS capacity for uniform distribution show similar tendencies.

- (ii)
The distribution of the (e)rtPS capacity has essential impact on the mean nrtPS packet delay.

These conclusions remain valid also in case of non-saturated BE traffic, since the BE traffic does not influence the nrtPS packet delay. This is due to the applied capacity allocation rule, in which the nrtPS traffic has priority over the BE traffic at the same SS.

The presented analytical model also enables to enforce specified upper bounds on the mean nrtPS packet delays at every SS in a specified range of loads. In this case, the optimal value of the total amount of real-time capacities can be determined.

In case of a more general QoS requirement (delay constraint), the optimal set of priority weights of the SSs can be determined by using a specific cost model (see Section 6.4).

## Declarations

### Acknowledgments

This work is supported by Tampere Graduate School in Information Science and Engineering, Nokia Foundation, and HPY Research Foundation.

## Authors’ Affiliations

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