根据mysql中的另一列添加序列号列

Question

我有一个包含以下表结构的表代码。 id是自动递增id，代码是随机唯一的15位数代码，customer_id是客户的id。该表有近13万行

 id      code    customer_id 
 1     123...4      1            
 2     124...5      1            
 3     128...3      1            
 4     234...1      2            
 5     678...3      2            
 6     567...8      1            

我在表中添加了一个列serial_number，我想添加一个serial_number，它将根据现有值的customer_id为下面各个客户的每个值递增。我如何在mysql中执行此操作？

 id    code       customer_id  serial_number
 1     123...4      1            1
 2     124...5      1            2
 3     128...3      1            3
 4     234...1      2            1
 5     678...3      2            2
 6     567...8      1            4     

我试过这种方法，但我的mysql连接正在超时：

MySQL: Add sequence column based on another field

CREATE temporary table serial_number ( id bigint, serial_number int);
INSERT INTO serial_number ( id, serial_number )
    SELECT id, 
      (SELECT count(*) + 1 FROM code c 
      WHERE c.id < code.id AND c.customer_id = code.customer_id) as    serial_number 
    FROM code;

UPDATE test INNER join serial_number ON code.id = serial_number.id SET   code.serial_number = serial_number.serial_number;

错误代码：2013。查询期间与MySQL服务器的连接丢失