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This paper considers the Poisson equation for general state-space Markovchains in continuous time. The main purpose of this paper is to presentspecific bounds for the solutions of the Poisson equation for generalstate-space Markov chains. The solutions of the Poisson equation are unique inthe sense that they are expressed in terms of a certain probabilisticallyinterpretable solution (called the {\it standard solution}). Thus, we establishsome specific bounds for the standard solution under the $f$-modulated driftcondition (which is a kind of Foster-Lyapunov-type condition) and some moderateconditions. To demonstrate the applicability of our results, we consider theworkload processes in two queues: MAP/GI/1 queue, and M/GI/1 queue withworkload capacity limit.

Specific bounds for a probabilistically interpretable solution of the  Poisson equation for general state-space Markov chains with queueing  applications