With Spring boot Dalston.SR3 (which uses open zipkin 1.28) you can achieve this by setting property zipkin.storage.mem.max-spans=xxx This will limit the number of spans and discard old ones.
pom.xml
<parent>
<groupId>org.springframework.boot</groupId>
<artifactId>spring-boot-starter-parent</artifactId>
<version>1.5.4.RELEASE</version>
<relativePath/> <!-- lookup parent from repository -->
</parent>
<properties>
<project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
<project.reporting.outputEncoding>UTF-8</project.reporting.outputEncoding>
<java.version>1.8</java.version>
<spring-cloud.version>Dalston.SR3</spring-cloud.version>
</properties>