Effect of Channel Conditions on Inventory Database Update in Supply Chains

Yazarlar: Murat Kocaoglu∗, Cuneyt Oksuz†, Ozgur B. Akan∗

∗ Next-generation and Wireless Communications Laboratory

Department of Electrical and Electronics Engineering, Koc University, Istanbul, Turkey

This work was supported in part by the Scientific and Technological Research Council of Turkey (TUBITAK) TEYDEB Program under Contract TEYDEB-7120977- JMobilVeri.

Introduction

The movement of a product from production to the customer is modeled inside the supply chain. Supply chain covers a wide range of processes in the lifecycle of a product from the supply of the raw material, to the movement of the product to the distributors and end users. For corporations, supply chain management is crucial. Optimization of the global supply chain is required to maximize the profit. An important process in the supply chain is the accurate update of the inventory database. Consider an inventory record, which is updated as goods are transferred from manufacturers to the distributors. Inaccurate update of the inventory database could lead to stockout and should be prevented to maximize the profit [1]. In general controlling whether the database updates contain error or not is costly for large databases. Even if an error is detected, it is hard to spot and correct it [2]. Thus, it is important that the transactions for database update are kept error-free. 

Today, wireless communications is an integral part of the supply chain. Information regarding the distribution of a product is transmitted from the distributors to the manufacturers via wireless and wired links. The accuracy of the stock database is crucial as even a small change’s effect on the profit is tremendous in the long run. Since checking the database for the accuracy of the entries is exhausting, especially for very large data sets, errors should be prevented before occuring, during the data transmission through the wireless communication channel, which constitutes the bottleneck of the communication link between the distributors and the manufacturers. As channel between the hand terminal and wireless access point that is used for the transmission of database update information is not always reliable, it is important to analyze the effects of the channel state and employed techniques to keep database error-free. To use the channel reliably, communication techniques that adapt themselves to the channel is necessary. In this paper, we analyze the effect of channel variations on the accuracy of the inventory database update. We show that employing adaptive error correction techniques could improve average end-to-end delay and database error rate. We consider a fading wireless channel with burst errors. Results show that depending on the reliability of the channel, we can adapt the employed error control coding scheme to reduce the delay, or erroneous update rate of the database. The paper is organized as follows: In Sec. II, we present the system model including the wireless communication link. Later, in Sec. III, we introduce the underlying end-to-end error control mechanism and evaluate its performance for varying parameters. In Sec. IV, we present the analytical evaluations of delay and packet error rate (PER). Lastly, in Sec. V, we present our simulations and compare them with analytical results.

System Model

Consider the scenario where a certain product of is sold to the distributor from the manufacturer. A database at the manufacturer contains the remaining quantity of a number of products in the stock. We want to update the manufacturer database each time a batch of products are sold to the distributor. A hand terminal, which scans the sold product, generates the information packets containing the type of the product and quantity of the sold units. The end-to-end communication link between the hand terminal and the inventory database is shown in Fig. 1. Hand terminals mostly use wireless communication to connect to a wireless access point. Since wired link is assumed to be reliable we only consider the errors and delays due to the wireless communication link.

Each transaction is represented with a binary k-tuple, i.e., kbits, which are called the sourcewords. A sourceword contains the product code and product quantity as shown in Fig. 2 and is generated at the hand terminal. Assume that the products are sold in base unit of 100. Then, by allocating 4 bits to the product amount, we can encode the sell of 100, 200, ...1600 number of products. A sample transaction is provided in the figure together with the corresponding database update. When the wireless communication channel is not reliable, there is the possibility that database will be updated erroneously. We show that errors depend on the channel state and employing adaptive communication techniques helps reduce the inventory error rate. The main challenge of using wireless medium is to deal with the time varying characteristics. In the literature, Gilbert-Elliot model is widely used to characterize the fading channel with burst errors [3]. In this model, channel state changes according to a two-state Markov chain as shown in Fig. 3. Here p,q,hg and hb represent the channel transition probability from bad to good state, channel transition probability from good to bad state, bit error probability in the good, and bit error probability in the bad states, respectively. In general in fading channels, p > q. For example, it is calculated that at pedestrian speeds of 20 km/h, p ≈ 10⁻³, whereas q ≈ 10⁻⁵ [3]. This assures that the channel is mostly in the good state where it occasionally drops to the deep fading state in which error probability is higher. In [4], authors derive an analytical expression using the simplified GE model to ease the analysis, in which they assume that the bit error probability is 0 in the good state, and bit error probability is 1 in the bad state. However, from an information theory perspective, bit error probability can at most be 0.5, as increasing it further actually increases the mutual information. This is trivial from the coin toss example. If we know that the channel state is in the deep fade, we can discard the result and toss a fair coin and still decode correct 50% of the time. Hence, we assume that bit error probability in the bad state is 0.5 and vary bit error probability in the good state in the wide range of from 10⁻⁶ to 10⁻¹.

Error Control and Correction

Error control and correction is a major research topic in the communications theory. Engineers have developed numerous techniques to detect and correct errors since Shannon. Error correction is mainly divided into two categories as forward error correction, i.e., FEC, and automatic repeat request, i.e., ARQ. FEC techniques exploit the idea of adding redundancy to the information to combat the effects of noise. In ARQ technique, packets are retransmitted depending on the packet acknowledgements received using the feedback channel to improve reliability. In modern communication systems, both of them are used to further decrease the packet error probability. In this work, we consider several channel codes together with a retransmission strategy. We obtain the variation of end-to-end delay and packet error probability at the inventory database with varying channel conditions. Let us first discuss the channel codes that we employ in the simulations section. For forward error correction, we only consider linear block codes. Linear block codes are important in coding theory due to the simplicity of encoding and decoding. A block code C contains a number of n-tuples called the codewords, which are used to encode the source information. Hence a code determines the set of channel codewords and the mapping between the source and channel codewords. Hamming distance between two codewords is defined as the number of bits at which they differ. Hamming distance of a code, or simply code distance, is the minimum Hamming distance among all the codeword pairs in the codebook. Code distance determines the error correction capability of a code. Employing minimum distance decoding, a channel code with Hamming distance of d can correct up to   d−1 2  .