Piotr Kiedrowski Institute of Telecommunication, University of Technology And Live Sciences in Bydgoszcz, Poland,
[email protected]
Easy applicable algorithm for accelerate reading process in AMR systems based on WSN solutions Summary. Presented method is applicable to conventional wireless sensor networks (WSN) protocols like flooding, that use a random delay to avoid simultaneous packet transmitting by a cluster of nodes. This paper show analytic methods for the adaptive randomising time delay in nodes. Effectiveness of proposed randomising method depends on the network topology and the nodes range. Proposed methods have been verified and tested in a real WSN.
1 Introduction A multi-hop technique is often used to increase a range in wireless systems. In sensor networks that the ISM (Industrial, Scientific, Medical) band is used in, due to little transmitting power, the multi-hop technique is becoming more significant. One of variety of multi-hop is a flooding routing protocol. Dominant faults of this method are waste energy and bandwidth when sending extra copies of data by nodes covering overlapping areas [1]. Due to this case this method is disqualified very often by some authors [2]. If energetic issue doesn’t occur (for example, if as sensor network nodes are watt-hour meters or if network is intended to use in short time, like in military sensor systems) there is proved that the flooding routing has got many advantages. The most important of them are mentioned below: - Effectiveness, guaranteed by sending extra packets, - resilience for disturbances, guaranteed by multi-paths between source and destination nodes, - no necessity to use complicated routing algorithms. The last feature is very profitable in case using sensor network in automatic meter reading (AMR) domain, where a memory deficit always occur, especially RAM memory, used also to encrypt sending data. 2 Communication scheme in a considering solution A node in a network may act as a source node, destination node, or a transfer node. After receiving a packet by a node, firstly, the address field is checked. If content of this field is different from the node address, the packet is transmitted. The packet is sent forward and the transfer node must remember and modify just the handover tag. Every time the packet is passed on, the handover number is decremented. The handover number together with constant, maximum value (set upon initial transmission) indicate the path length. A mediating node pass to transmit packet procedure after expiring a short virtual period of time τV [3], enabling to detect back information sending by the destination node. If the mediating node doesn’t detect the destination node reaction, then the packet procedure transmitting will be activated. The main task of this procedure is to determine a random delay time TD from the range of 0 to τ, with simultaneous carrier detect (CD) status monitoring. If during the TD period of time no CD case occurs, a delivered packet will be transmitted after the TD period of time expires. In case CD occurs, the TD value will be increase by τV only when TD< τV in another case TD remains the same. The necessity of randomisation treatment is a consequence of avoiding simultaneous packet transmitting by a cluster of nodes. The expected value of packet transferring time by cluster (not by node) depends on the amount of nodes in this cluster that are able to transfer a packet of data effectively. This expected value can be defined by the formula presented below:
TED (m) = τ V +
τ m +1
,
where: m – a number of nodes in cluster that are able to transfer a packet effectively.
Including the fact that the τV value is much less than the TD value , TED will be determined without the τV component as is shown below: TED (m) =
τ
m +1
(1)
.
A maximal communication period of time from the source node to the destination node depends on: a number of hops – h, values of τ and τ V and the packet transmission time TTX can be defined by the formula shown below: Tcomm _ max = h (τ + τ V + TTX ) . (2) Probability of a maximal communication time period between nodes is determined by value Ph, where P is probability of delay time TD = τ in each transferring node. An expecting value of time communication period Tcomm_E between two nodes can be defined by replacing the τ value in the formula (2) by the TED(m) value defined in the formula (1) that is different in each hop, what is shown below: h
Tcomm _ E = h(τ V + TTX ) + τ ∑ i =1
1 . mi + 1
(3)
After analysing (3) there is possible to formulate a following statement: bigger node clusters (that are able to transfer a packet on communication path effectively) enable communication faster. In the formula (3) there is not taken into account simultaneity issue, signifying rising probability of collision occur if during transmitting the same packet many nodes participate. If in packet transmitting process, only one node participates, probability of collision will amount to 0, but TED will achieve the maximal value. These three issues mentioned above have been used to formulate a problem.
3 Problem definition How to determinate cluster size and trade it on to decrease the τ value, taking into account a fact that decreasing the τ value, increases probability of collision occurrence. This issue should be considered from a node’s point of view instead of all network. The last sentence comes out of network topology variation. 4 Decisive factors of probability value collision occurrence Factors that have main influence on collision appearance probability: - constant τ value (described earlier), - k – number of nodes in a cluster transferring the same received packet, - t – period of time during which the CD status can’t be monitored by node. The τ value is a constant, system value, usually the same for each node. The τ value comes out of established and represents maximal awaiting period of time. Independently, reducing the τ value to the τ’ value by single nodes bring about reducing a communication time; what on the other hand causes increasing collision probability[4]. The k value is a variable determined by a node in each communication process, relying on this variable, the node can define cluster size that takes place in. More transferring nodes bring about
increasing collision probability [4]. Relaying on the k value, a node determines the τ’ value what is an adaptation to conditions in which this node works. There also the fact that k ≥ m should be included because the k value is an amount of nodes that can transfer effective and ineffective. The t value arises from the node construction, especially from transceiver device. In this issue, this value should be included without any influence on it. If the t value is becoming less, then probability of collision decreases. 4 Defining a threshold value of collision occurring probability The threshold value of collision probability has been determined basing on assumed probability of collision occurring in each place all communication series. This value has been defined at level of 0,01. The main reason of acceptance this threshold value is a fact that in many application, exactly this value used to be applied as unreliability measure, which is used to determine threshold parameters; for example in [5] value of PER=10-2 (Packet Error Ratio). In case assuming the value of Pc_chain=0,01 for the h number of hops, the threshold value of collision occurrence probability in a single hop, may be defined by the formula presented below: Pc _ chain = 1 − (1 − Pc )h or Pc = 1 − h 1 − Pc _ chain .
(4)
For defined values: Pc_chain=10-2 and h=8, the threshold value Pc ≅ 0,125 ⋅ 10 −2 . The Pc value as a static value in connection to the variable k value is used by a node to the adaptive τ’ value defining, basing on the algorithm described below.
5 Adaptive algorithm of τ’ value determining This algorithm has been prepared basing on collision influence on communication effectiveness described in [4], [6]. Below there is presented a formula defining connections between Pc, k, τ’ and t values. This formula has been prepared basing on determining simultaneity coefficient method, taking the advantage of variance quotient without and with repetitions. τ ' τ ' τ ' τ ' ⋅ − 1 ⋅ − 2 ⋅ ... ⋅ − k + 1 t t t t . PC (k ,τ ' , t ) = 1 − k τ ' t Basing on (5) for static values of determined Pc_chain=10-2
(5)
and h=8, what gives from (4) τ' Pc = 0,125 ⋅ 10 −2 , below, on figure 1, there is presented connections curve to k. t
Fig.1. Characteristic of
τ' t
value to number of nodes in a cluster, for Pc_chain=10-2 and h=8
There is possible to determine the τ’ value by a network node, basing on known t value and updated k value. However there is not allowed to take advantage of the formula (5) directly in a node, because of too much RAM memory consuming rate by complicated floating points calculations. In proposed algorithm the node takes advantage of one-dimensional table (written and saved in EEPROM memory), which contains τ’ values, number of table element defines the k value. A t value is imposed because results from hardware solutions.
6 The algorithm implementation example Assuming in accepted resolution following values: h=8, Tcomm_max=6 s, TTX=13 ms (64 B with bit rate of 38400 bps), and TV has negligible effect on (2) , there is possible to determine the τ value, which in considered example amounts to 0.734 s. After analyzing actual hardware solutions the t variable may achieve values in range from a few µs to about 1 ms. Hardware equipment that has been used to verify achieved research results guaranteed detecting CD with edge value below 5 µs. τ 0.734 s There is possible, basing on the = ≅ 148 ⋅ 103 quotient to determine the maximal t 5µs nodes number kmax, after exceed which, the adaptive randomisation method is high – risk, because of collision occurrence. In described example, assuming (4) and (5) or data from a diagram presented on figure 1 (just because the same number of hops) the kmax value is 19. A one-dimensional table will contain 19 τ’ value elements calculated basing on (5). These values formulated in milliseconds and rounded up to integer value are: 12, 24, 40, 60, 85, 114, 144, 179, 219, 264, 311, 363, 418, 478, 545, 610, 675, 756 and 831. This is obvious that an initiating τ’ value should be the maximal value - τ. 7 Conclusion The adaptive randomising time delay method, proposed in this paper, has been prepared by analytic methods. Proposed solution is general and can be applied in different solutions in wireless sensor networks based on multi-hop technique. The activity range of proposed methods comes out of presented algorithm and other protocol parameters (for example maximum numbers of hops or assumed Pc_chain value).
Effectiveness of proposed randomising method depends on the network topology and the nodes range. In most cases this method may be regarded as very effective. Proposed method is especially efficient in real AMR systems, where a mesh network topology used to be typical. Very important also are facts that software implement methods in sensor network nodes used to verify and tests, increased demand for RAM memory merely on 20 bytes and that described methods can be used both by networks contain nodes with the old software, and nodes, where the adaptive method was implemented. References 1. Al-Karaki JN, Kamal AN (2004) Routing techniques in wireless sensor networks: a survey. Wireless Communications IEEE, vol. 11, Issue 6: 6-28 2. Ilyas M, Mahgoub I (2005) Handbook of Sensor Networks: Compact Wireless and Wired Sensing Systems. CRC Press 3. Nowicki J, Woźniak K (2000) Sieci LAN, MAN i WAN – protokoły komunikacyjne. Wydawnictwo Fundacji Postępu Telekomunikacji 4. Boryna B, Bratkowski A, Kiedrowski P (2008) Istota monitorowania nośnej i liczby węzłów sąsiednich, a skuteczność komunikacji w systemach AMR opartych na sieciach WSN. Przegląd Telekomunikacyjny – Wiadomości Telekomunikacyjne, nr 8/9 2008: 1207-1214 5. Texas Instruments (2006) CC1100 Single Chip Low cost Low Power RF Transceiver. Texas Instruments Incorporated: 89-90 6. Boryna B, Kiedrowski P (2007) Wpływ kolizji na skuteczność odczytów liczników energii elektrycznej. Zeszyty Naukowe Wydziału Elektroniki, Telekomunikacji i Informatyki Politechniki Gdańskiej nr 1: 147-150
