A Discrete-Event Network Simulator
API
80211e-txop.cc
Go to the documentation of this file.
1 /* -*- Mode:C++; c-file-style:"gnu"; indent-tabs-mode:nil; -*- */
2 /*
3  * Copyright (c) 2016 Sébastien Deronne
4  *
5  * This program is free software; you can redistribute it and/or modify
6  * it under the terms of the GNU General Public License version 2 as
7  * published by the Free Software Foundation;
8  *
9  * This program is distributed in the hope that it will be useful,
10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12  * GNU General Public License for more details.
13  *
14  * You should have received a copy of the GNU General Public License
15  * along with this program; if not, write to the Free Software
16  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17  *
18  * Author: Sébastien Deronne <sebastien.deronne@gmail.com>
19  */
20 
21 #include "ns3/core-module.h"
22 #include "ns3/network-module.h"
23 #include "ns3/applications-module.h"
24 #include "ns3/wifi-module.h"
25 #include "ns3/mobility-module.h"
26 #include "ns3/internet-module.h"
27 
28 // This is an example that illustrates 802.11 QoS for different Access Categories.
29 // It defines 4 independant Wi-Fi networks (working on different logical channels
30 // on the same "ns3::YansWifiPhy" channel object).
31 // Each network contains one access point and one station. Each station continuously
32 // transmits data packets to its respective AP.
33 //
34 // Network topology (numbers in parentheses are channel numbers):
35 //
36 // BSS A (36) BSS B (40) BSS C (44) BSS D (48)
37 // * * * * * * * *
38 // | | | | | | | |
39 // AP A STA A AP B STA B AP C STA C AP D STA D
40 //
41 // The configuration is the following on the 4 networks:
42 // - STA A sends AC_BE traffic to AP A with default AC_BE TXOP value of 0 (1 MSDU);
43 // - STA B sends AC_BE traffic to AP B with non-default AC_BE TXOP of 3.008 ms;
44 // - STA C sends AC_VI traffic to AP C with default AC_VI TXOP of 3.008 ms;
45 // - STA D sends AC_VI traffic to AP D with non-default AC_VI TXOP value of 0 (1 MSDU);
46 //
47 // The user can select the distance between the stations and the APs, can enable/disable the RTS/CTS mechanism
48 // and can choose the payload size and the simulation duration.
49 // Example: ./waf --run "80211e-txop --distance=10 --enableRts=0 --simulationTime=20 --payloadSize=1000"
50 //
51 // The output prints the throughput measured for the 4 cases/networks decribed above. When TXOP is enabled, results show
52 // increased throughput since the channel is granted for a longer duration. TXOP is enabled by default for AC_VI and AC_VO,
53 // so that they can use the channel for a longer duration than AC_BE and AC_BK.
54 
55 using namespace ns3;
56 
57 NS_LOG_COMPONENT_DEFINE ("80211eTxop");
58 
59 int main (int argc, char *argv[])
60 {
61  uint32_t payloadSize = 1472; //bytes
62  uint64_t simulationTime = 10; //seconds
63  double distance = 5; //meters
64  bool enablePcap = 0;
65 
67  cmd.AddValue ("payloadSize", "Payload size in bytes", payloadSize);
68  cmd.AddValue ("simulationTime", "Simulation time in seconds", simulationTime);
69  cmd.AddValue ("distance", "Distance in meters between the station and the access point", distance);
70  cmd.AddValue ("enablePcap", "Enable/disable pcap file generation", enablePcap);
71  cmd.Parse (argc, argv);
72 
73  NodeContainer wifiStaNode;
74  wifiStaNode.Create (4);
76  wifiApNode.Create (4);
77 
81  phy.SetChannel (channel.Create ());
82 
83  WifiHelper wifi; //the default standard of 802.11a will be selected by this helper since the program doesn't specify another one
84  wifi.SetRemoteStationManager ("ns3::IdealWifiManager");
86 
87  NetDeviceContainer staDeviceA, staDeviceB, staDeviceC, staDeviceD, apDeviceA, apDeviceB, apDeviceC, apDeviceD;
88  Ssid ssid;
89 
90  //Network A
91  ssid = Ssid ("network-A");
92  phy.Set ("ChannelNumber", UintegerValue(36));
93  mac.SetType ("ns3::StaWifiMac",
94  "QosSupported", BooleanValue (true),
95  "Ssid", SsidValue (ssid));
96  staDeviceA = wifi.Install (phy, mac, wifiStaNode.Get(0));
97 
98  mac.SetType ("ns3::ApWifiMac",
99  "QosSupported", BooleanValue (true),
100  "Ssid", SsidValue (ssid),
101  "BeaconGeneration", BooleanValue (true));
102  apDeviceA = wifi.Install (phy, mac, wifiApNode.Get(0));
103 
104  //Network B
105  ssid = Ssid ("network-B");
106  phy.Set ("ChannelNumber", UintegerValue(40));
107  mac.SetType ("ns3::StaWifiMac",
108  "QosSupported", BooleanValue (true),
109  "Ssid", SsidValue (ssid));
110 
111  staDeviceB = wifi.Install (phy, mac, wifiStaNode.Get(1));
112 
113  mac.SetType ("ns3::ApWifiMac",
114  "QosSupported", BooleanValue (true),
115  "Ssid", SsidValue (ssid),
116  "BeaconGeneration", BooleanValue (true));
117  apDeviceB = wifi.Install (phy, mac, wifiApNode.Get(1));
118 
119  //Modify EDCA configuration (TXOP limit) for AC_BE
120  Ptr<NetDevice> dev = wifiApNode.Get(1)->GetDevice(0);
121  Ptr<WifiNetDevice> wifi_dev = DynamicCast<WifiNetDevice>(dev);
122  Ptr<WifiMac> wifi_mac = wifi_dev->GetMac();
123  PointerValue ptr;
124  Ptr<EdcaTxopN> edca;
125  wifi_mac->GetAttribute("BE_EdcaTxopN", ptr);
126  edca = ptr.Get<EdcaTxopN>();
127  edca->SetTxopLimit (MicroSeconds (3008));
128 
129  //Network C
130  ssid = Ssid ("network-C");
131  phy.Set ("ChannelNumber", UintegerValue(44));
132  mac.SetType ("ns3::StaWifiMac",
133  "QosSupported", BooleanValue (true),
134  "Ssid", SsidValue (ssid));
135 
136  staDeviceC = wifi.Install (phy, mac, wifiStaNode.Get(2));
137 
138  mac.SetType ("ns3::ApWifiMac",
139  "QosSupported", BooleanValue (true),
140  "Ssid", SsidValue (ssid),
141  "BeaconGeneration", BooleanValue (true));
142  apDeviceC = wifi.Install (phy, mac, wifiApNode.Get(2));
143 
144  //Network D
145  ssid = Ssid ("network-D");
146  phy.Set ("ChannelNumber", UintegerValue(48));
147  mac.SetType ("ns3::StaWifiMac",
148  "QosSupported", BooleanValue (true),
149  "Ssid", SsidValue (ssid));
150 
151  staDeviceD = wifi.Install (phy, mac, wifiStaNode.Get(3));
152 
153  mac.SetType ("ns3::ApWifiMac",
154  "QosSupported", BooleanValue (true),
155  "Ssid", SsidValue (ssid),
156  "BeaconGeneration", BooleanValue (true));
157  apDeviceD = wifi.Install (phy, mac, wifiApNode.Get(3));
158 
159  //Modify EDCA configuration (TXOP limit) for AC_VO
160  dev = wifiApNode.Get(3)->GetDevice(0);
161  wifi_dev = DynamicCast<WifiNetDevice>(dev);
162  wifi_mac = wifi_dev->GetMac();
163  wifi_mac->GetAttribute("VI_EdcaTxopN", ptr);
164  edca = ptr.Get<EdcaTxopN>();
165  edca->SetTxopLimit (MicroSeconds (0));
166 
167  /* Setting mobility model */
169  Ptr<ListPositionAllocator> positionAlloc = CreateObject<ListPositionAllocator> ();
170  mobility.SetMobilityModel ("ns3::ConstantPositionMobilityModel");
171 
172  //Set position for APs
173  positionAlloc->Add (Vector (0.0, 0.0, 0.0));
174  positionAlloc->Add (Vector (10.0, 0.0, 0.0));
175  positionAlloc->Add (Vector (20.0, 0.0, 0.0));
176  positionAlloc->Add (Vector (30.0, 0.0, 0.0));
177  //Set position for STAs
178  positionAlloc->Add (Vector (distance, 0.0, 0.0));
179  positionAlloc->Add (Vector (10 + distance, 0.0, 0.0));
180  positionAlloc->Add (Vector (20 + distance, 0.0, 0.0));
181  positionAlloc->Add (Vector (30 + distance, 0.0, 0.0));
182  //Remark: while we set these positions 10 meters apart, the networks do not interact
183  //and the only variable that affects transmission performance is the distance.
184 
185  mobility.SetPositionAllocator (positionAlloc);
186  mobility.Install (wifiApNode);
187  mobility.Install (wifiStaNode);
188 
189  /* Internet stack */
191  stack.Install (wifiApNode);
192  stack.Install (wifiStaNode);
193 
195 
196  address.SetBase ("192.168.1.0", "255.255.255.0");
197  Ipv4InterfaceContainer StaInterfaceA;
198  StaInterfaceA = address.Assign (staDeviceA);
199  Ipv4InterfaceContainer ApInterfaceA;
200  ApInterfaceA = address.Assign (apDeviceA);
201 
202  address.SetBase ("192.168.2.0", "255.255.255.0");
203  Ipv4InterfaceContainer StaInterfaceB;
204  StaInterfaceB = address.Assign (staDeviceB);
205  Ipv4InterfaceContainer ApInterfaceB;
206  ApInterfaceB = address.Assign (apDeviceB);
207 
208  address.SetBase ("192.168.3.0", "255.255.255.0");
209  Ipv4InterfaceContainer StaInterfaceC;
210  StaInterfaceC = address.Assign (staDeviceC);
211  Ipv4InterfaceContainer ApInterfaceC;
212  ApInterfaceC = address.Assign (apDeviceC);
213 
214  address.SetBase ("192.168.4.0", "255.255.255.0");
215  Ipv4InterfaceContainer StaInterfaceD;
216  StaInterfaceD = address.Assign (staDeviceD);
217  Ipv4InterfaceContainer ApInterfaceD;
218  ApInterfaceD = address.Assign (apDeviceD);
219 
220  /* Setting applications */
221  UdpServerHelper myServerA (5001);
222  ApplicationContainer serverAppA = myServerA.Install (wifiApNode.Get (0));
223  serverAppA.Start (Seconds (0.0));
224  serverAppA.Stop (Seconds (simulationTime + 1));
225 
226  InetSocketAddress destA (ApInterfaceA.GetAddress (0), 5001);
227  destA.SetTos (0x70); //AC_BE
228 
229  OnOffHelper myClientA ("ns3::UdpSocketFactory", destA);
230  myClientA.SetAttribute ("OnTime", StringValue ("ns3::ConstantRandomVariable[Constant=1]"));
231  myClientA.SetAttribute ("OffTime", StringValue ("ns3::ConstantRandomVariable[Constant=0]"));
232  myClientA.SetAttribute ("DataRate", StringValue("100000kb/s"));
233  myClientA.SetAttribute ("PacketSize", UintegerValue(payloadSize));
234 
235  ApplicationContainer clientAppA = myClientA.Install (wifiStaNode.Get (0));
236  clientAppA.Start (Seconds (1.0));
237  clientAppA.Stop (Seconds (simulationTime + 1));
238 
239  UdpServerHelper myServerB (5001);
240  ApplicationContainer serverAppB = myServerB.Install (wifiApNode.Get (1));
241  serverAppB.Start (Seconds (0.0));
242  serverAppB.Stop (Seconds (simulationTime + 1));
243 
244  InetSocketAddress destB (ApInterfaceB.GetAddress (0), 5001);
245  destB.SetTos (0x70); //AC_BE
246 
247  OnOffHelper myClientB ("ns3::UdpSocketFactory", destB);
248  myClientB.SetAttribute ("OnTime", StringValue ("ns3::ConstantRandomVariable[Constant=1]"));
249  myClientB.SetAttribute ("OffTime", StringValue ("ns3::ConstantRandomVariable[Constant=0]"));
250  myClientB.SetAttribute ("DataRate", StringValue("100000kb/s"));
251  myClientB.SetAttribute ("PacketSize", UintegerValue(payloadSize));
252 
253  ApplicationContainer clientAppB = myClientB.Install (wifiStaNode.Get (1));
254  clientAppB.Start (Seconds (1.0));
255  clientAppB.Stop (Seconds (simulationTime + 1));
256 
257  UdpServerHelper myServerC (5001);
258  ApplicationContainer serverAppC = myServerC.Install (wifiApNode.Get (2));
259  serverAppC.Start (Seconds (0.0));
260  serverAppC.Stop (Seconds (simulationTime + 1));
261 
262  InetSocketAddress destC (ApInterfaceC.GetAddress (0), 5001);
263  destC.SetTos (0xb8); //AC_VI
264 
265  OnOffHelper myClientC ("ns3::UdpSocketFactory", destC);
266  myClientC.SetAttribute ("OnTime", StringValue ("ns3::ConstantRandomVariable[Constant=1]"));
267  myClientC.SetAttribute ("OffTime", StringValue ("ns3::ConstantRandomVariable[Constant=0]"));
268  myClientC.SetAttribute ("DataRate", StringValue("100000kb/s"));
269  myClientC.SetAttribute ("PacketSize", UintegerValue(payloadSize));
270 
271  ApplicationContainer clientAppC = myClientC.Install (wifiStaNode.Get (2));
272  clientAppC.Start (Seconds (1.0));
273  clientAppC.Stop (Seconds (simulationTime + 1));
274 
275  UdpServerHelper myServerD (5001);
276  ApplicationContainer serverAppD = myServerD.Install (wifiApNode.Get (3));
277  serverAppD.Start (Seconds (0.0));
278  serverAppD.Stop (Seconds (simulationTime + 1));
279 
280  InetSocketAddress destD (ApInterfaceD.GetAddress (0), 5001);
281  destD.SetTos (0xb8); //AC_VI
282 
283  OnOffHelper myClientD ("ns3::UdpSocketFactory", destD);
284  myClientD.SetAttribute ("OnTime", StringValue ("ns3::ConstantRandomVariable[Constant=1]"));
285  myClientD.SetAttribute ("OffTime", StringValue ("ns3::ConstantRandomVariable[Constant=0]"));
286  myClientD.SetAttribute ("DataRate", StringValue("100000kb/s"));
287  myClientD.SetAttribute ("PacketSize", UintegerValue(payloadSize));
288 
289  ApplicationContainer clientAppD = myClientD.Install (wifiStaNode.Get (3));
290  clientAppD.Start (Seconds (1.0));
291  clientAppD.Stop (Seconds (simulationTime + 1));
292 
293  if (enablePcap)
294  {
295  phy.EnablePcap ("AP_A", apDeviceA.Get (0));
296  phy.EnablePcap ("STA_A", staDeviceA.Get (0));
297  phy.EnablePcap ("AP_B", apDeviceB.Get (0));
298  phy.EnablePcap ("STA_B", staDeviceB.Get (0));
299  phy.EnablePcap ("AP_C", apDeviceC.Get (0));
300  phy.EnablePcap ("STA_C", staDeviceC.Get (0));
301  phy.EnablePcap ("AP_D", apDeviceD.Get (0));
302  phy.EnablePcap ("STA_D", staDeviceD.Get (0));
303  }
304 
305  Simulator::Stop (Seconds (simulationTime + 1));
306  Simulator::Run ();
308 
309  /* Show results */
310  uint32_t totalPacketsThrough = DynamicCast<UdpServer> (serverAppA.Get (0))->GetReceived ();
311  double throughput = totalPacketsThrough * payloadSize * 8 / (simulationTime * 1000000.0);
312  std::cout << "Throughput for AC_BE with default TXOP limit (0ms): " << throughput << " Mbit/s" << '\n';
313 
314  totalPacketsThrough = DynamicCast<UdpServer> (serverAppB.Get (0))->GetReceived ();
315  throughput = totalPacketsThrough * payloadSize * 8 / (simulationTime * 1000000.0);
316  std::cout << "Throughput for AC_BE with non-default TXOP limit (3.008ms): " << throughput << " Mbit/s" << '\n';
317 
318  totalPacketsThrough = DynamicCast<UdpServer> (serverAppC.Get (0))->GetReceived ();
319  throughput = totalPacketsThrough * payloadSize * 8 / (simulationTime * 1000000.0);
320  std::cout << "Throughput for AC_VI with default TXOP limit (3.008ms): " << throughput << " Mbit/s" << '\n';
321 
322  totalPacketsThrough = DynamicCast<UdpServer> (serverAppD.Get (0))->GetReceived ();
323  throughput = totalPacketsThrough * payloadSize * 8 / (simulationTime * 1000000.0);
324  std::cout << "Throughput for AC_VI with non-default TXOP limit (0ms): " << throughput << " Mbit/s" << '\n';
325 
326  return 0;
327 }
tuple channel
Definition: third.py:85
void Set(std::string name, const AttributeValue &v)
Definition: wifi-helper.cc:112
holds a vector of ns3::Application pointers.
Ptr< T > Get(void) const
Definition: pointer.h:194
an Inet address class
Smart pointer class similar to boost::intrusive_ptr.
Definition: ptr.h:73
AttributeValue implementation for Boolean.
Definition: boolean.h:34
holds a vector of std::pair of Ptr and interface index.
Ptr< YansWifiChannel > Create(void) const
void SetRemoteStationManager(std::string type, std::string n0="", const AttributeValue &v0=EmptyAttributeValue(), std::string n1="", const AttributeValue &v1=EmptyAttributeValue(), std::string n2="", const AttributeValue &v2=EmptyAttributeValue(), std::string n3="", const AttributeValue &v3=EmptyAttributeValue(), std::string n4="", const AttributeValue &v4=EmptyAttributeValue(), std::string n5="", const AttributeValue &v5=EmptyAttributeValue(), std::string n6="", const AttributeValue &v6=EmptyAttributeValue(), std::string n7="", const AttributeValue &v7=EmptyAttributeValue())
Definition: wifi-helper.cc:683
Hold variables of type string.
Definition: string.h:41
Ptr< NetDevice > Get(uint32_t i) const
Get the Ptr stored in this container at a given index.
Make it easy to create and manage PHY objects for the yans model.
static YansWifiChannelHelper Default(void)
Create a channel helper in a default working state.
bool enablePcap
static void Run(void)
Run the simulation.
Definition: simulator.cc:201
#define NS_LOG_COMPONENT_DEFINE(name)
Define a Log component with a specific name.
Definition: log.h:201
aggregate IP/TCP/UDP functionality to existing Nodes.
static YansWifiPhyHelper Default(void)
Create a phy helper in a default working state.
helps to create WifiNetDevice objects
Definition: wifi-helper.h:231
A helper to make it easier to instantiate an ns3::OnOffApplication on a set of nodes.
Definition: on-off-helper.h:42
tuple cmd
Definition: second.py:35
void SetPcapDataLinkType(enum SupportedPcapDataLinkTypes dlt)
Set the data link type of PCAP traces to be used.
Definition: wifi-helper.cc:530
virtual NetDeviceContainer Install(const WifiPhyHelper &phy, const WifiMacHelper &mac, NodeContainer c) const
Definition: wifi-helper.cc:712
void SetChannel(Ptr< YansWifiChannel > channel)
This queue contains packets for a particular access class.
Definition: edca-txop-n.h:86
void Install(Ptr< Node > node) const
"Layout" a single node according to the current position allocator type.
tuple mobility
Definition: third.py:101
tuple phy
Definition: third.py:86
Hold an unsigned integer type.
Definition: uinteger.h:44
holds a vector of ns3::NetDevice pointers
Create a server application which waits for input UDP packets and uses the information carried into t...
Ptr< NetDevice > GetDevice(uint32_t index) const
Retrieve the index-th NetDevice associated to this node.
Definition: node.cc:142
tuple mac
Definition: third.py:92
void Start(Time start)
Arrange for all of the Applications in this container to Start() at the Time given as a parameter...
Parse command-line arguments.
Definition: command-line.h:205
static void Destroy(void)
Execute the events scheduled with ScheduleDestroy().
Definition: simulator.cc:165
tuple wifiApNode
Definition: third.py:83
Every class exported by the ns3 library is enclosed in the ns3 namespace.
keep track of a set of node pointers.
Ptr< Application > Get(uint32_t i) const
Get the Ptr stored in this container at a given index.
Hold objects of type Ptr.
Definition: pointer.h:36
void SetMobilityModel(std::string type, std::string n1="", const AttributeValue &v1=EmptyAttributeValue(), std::string n2="", const AttributeValue &v2=EmptyAttributeValue(), std::string n3="", const AttributeValue &v3=EmptyAttributeValue(), std::string n4="", const AttributeValue &v4=EmptyAttributeValue(), std::string n5="", const AttributeValue &v5=EmptyAttributeValue(), std::string n6="", const AttributeValue &v6=EmptyAttributeValue(), std::string n7="", const AttributeValue &v7=EmptyAttributeValue(), std::string n8="", const AttributeValue &v8=EmptyAttributeValue(), std::string n9="", const AttributeValue &v9=EmptyAttributeValue())
void Install(std::string nodeName) const
Aggregate implementations of the ns3::Ipv4, ns3::Ipv6, ns3::Udp, and ns3::Tcp classes onto the provid...
tuple ssid
Definition: third.py:93
manage and create wifi channel objects for the yans model.
void GetAttribute(std::string name, AttributeValue &value) const
Get the value of an attribute, raising fatal errors if unsuccessful.
Definition: object-base.cc:229
create MAC layers for a ns3::WifiNetDevice.
tuple stack
Definition: first.py:34
The IEEE 802.11 SSID Information Element.
Definition: ssid.h:38
virtual void SetType(std::string type, std::string n0="", const AttributeValue &v0=EmptyAttributeValue(), std::string n1="", const AttributeValue &v1=EmptyAttributeValue(), std::string n2="", const AttributeValue &v2=EmptyAttributeValue(), std::string n3="", const AttributeValue &v3=EmptyAttributeValue(), std::string n4="", const AttributeValue &v4=EmptyAttributeValue(), std::string n5="", const AttributeValue &v5=EmptyAttributeValue(), std::string n6="", const AttributeValue &v6=EmptyAttributeValue(), std::string n7="", const AttributeValue &v7=EmptyAttributeValue(), std::string n8="", const AttributeValue &v8=EmptyAttributeValue(), std::string n9="", const AttributeValue &v9=EmptyAttributeValue(), std::string n10="", const AttributeValue &v10=EmptyAttributeValue())
Helper class used to assign positions and mobility models to nodes.
void Stop(Time stop)
Arrange for all of the Applications in this container to Stop() at the Time given as a parameter...
Ipv4InterfaceContainer Assign(const NetDeviceContainer &c)
Assign IP addresses to the net devices specified in the container based on the current network prefix...
void AddValue(const std::string &name, const std::string &help, T &value)
Add a program argument, assigning to POD.
Definition: command-line.h:495
static void Stop(void)
Tell the Simulator the calling event should be the last one executed.
Definition: simulator.cc:209
Ptr< Node > Get(uint32_t i) const
Get the Ptr stored in this container at a given index.
Time Seconds(double value)
Construct a Time in the indicated unit.
Definition: nstime.h:895
AttributeValue implementation for Ssid.
Definition: ssid.h:95
void Add(Vector v)
Add a position to the list of positions.
Ptr< WifiMac > GetMac(void) const
void Parse(int argc, char *argv[])
Parse the program arguments.
A helper class to make life easier while doing simple IPv4 address assignment in scripts.
Time MicroSeconds(uint64_t value)
Construct a Time in the indicated unit.
Definition: nstime.h:911
tuple wifi
Definition: third.py:89
void Create(uint32_t n)
Create n nodes and append pointers to them to the end of this NodeContainer.
tuple address
Definition: first.py:37
void EnablePcap(std::string prefix, Ptr< NetDevice > nd, bool promiscuous=false, bool explicitFilename=false)
Enable pcap output the indicated net device.
virtual void SetTxopLimit(Time txopLimit)
Definition: edca-txop-n.cc:413
void SetPositionAllocator(Ptr< PositionAllocator > allocator)
Set the position allocator which will be used to allocate the initial position of every node initiali...
Include Radiotap link layer information.
Definition: wifi-helper.h:117
void SetBase(Ipv4Address network, Ipv4Mask mask, Ipv4Address base="0.0.0.1")
Set the base network number, network mask and base address.
Ipv4Address GetAddress(uint32_t i, uint32_t j=0) const