diff --git a/src/backend/distributed/planner/distributed_planner.c b/src/backend/distributed/planner/distributed_planner.c
index b31f29d3d..68b3a17b7 100644
--- a/src/backend/distributed/planner/distributed_planner.c
+++ b/src/backend/distributed/planner/distributed_planner.c
@@ -124,7 +124,6 @@ static PlannerRestrictionContext * CurrentPlannerRestrictionContext(void);
 static void PopPlannerRestrictionContext(void);
 static void ResetPlannerRestrictionContext(
 	PlannerRestrictionContext *plannerRestrictionContext);
-static bool HasUnresolvedExternParamsWalker(Node *expression, ParamListInfo boundParams);
 static bool IsLocalReferenceTableJoin(Query *parse, List *rangeTableList);
 static bool QueryIsNotSimpleSelect(Node *node);
 static void UpdateReferenceTablesWithShard(List *rangeTableList);
@@ -2242,7 +2241,7 @@ ResetPlannerRestrictionContext(PlannerRestrictionContext *plannerRestrictionCont
  * has external parameters that are not contained in boundParams, false
  * otherwise.
  */
-static bool
+bool
 HasUnresolvedExternParamsWalker(Node *expression, ParamListInfo boundParams)
 {
 	if (expression == NULL)
diff --git a/src/backend/distributed/planner/multi_physical_planner.c b/src/backend/distributed/planner/multi_physical_planner.c
index dc359881c..d8861da18 100644
--- a/src/backend/distributed/planner/multi_physical_planner.c
+++ b/src/backend/distributed/planner/multi_physical_planner.c
@@ -2130,12 +2130,29 @@ BuildJobTreeTaskList(Job *jobTree, PlannerRestrictionContext *plannerRestriction
 		List *assignedSqlTaskList = AssignTaskList(sqlTaskList);
 		AssignDataFetchDependencies(assignedSqlTaskList);
 
-		/* now assign merge task's data fetch dependencies */
+		/* if the parameters has not been resolved, record it */
+		job->parametersInJobQueryResolved =
+			!HasUnresolvedExternParamsWalker((Node *) job->jobQuery, NULL);
+
+		/*
+		 * Make final adjustments for the assigned tasks.
+		 *
+		 * First, update SELECT tasks' parameters resolved field.
+		 *
+		 * Second, assign merge task's data fetch dependencies.
+		 */
 		foreach(assignedSqlTaskCell, assignedSqlTaskList)
 		{
 			Task *assignedSqlTask = (Task *) lfirst(assignedSqlTaskCell);
-			List *assignedMergeTaskList = FindDependentMergeTaskList(assignedSqlTask);
 
+			/* we don't support parameters in the physical planner */
+			if (assignedSqlTask->taskType == SELECT_TASK)
+			{
+				assignedSqlTask->parametersInQueryStringResolved =
+					job->parametersInJobQueryResolved;
+			}
+
+			List *assignedMergeTaskList = FindDependentMergeTaskList(assignedSqlTask);
 			AssignDataFetchDependencies(assignedMergeTaskList);
 		}
 
diff --git a/src/include/distributed/distributed_planner.h b/src/include/distributed/distributed_planner.h
index 578d2bfa1..f08ebd094 100644
--- a/src/include/distributed/distributed_planner.h
+++ b/src/include/distributed/distributed_planner.h
@@ -196,6 +196,7 @@ extern void multi_join_restriction_hook(PlannerInfo *root,
 										RelOptInfo *innerrel,
 										JoinType jointype,
 										JoinPathExtraData *extra);
+extern bool HasUnresolvedExternParamsWalker(Node *expression, ParamListInfo boundParams);
 extern bool IsModifyCommand(Query *query);
 extern bool IsModifyDistributedPlan(struct DistributedPlan *distributedPlan);
 extern void EnsurePartitionTableNotReplicated(Oid relationId);
diff --git a/src/test/regress/expected/local_shard_execution.out b/src/test/regress/expected/local_shard_execution.out
index 7e1fb892e..9e8639d7d 100644
--- a/src/test/regress/expected/local_shard_execution.out
+++ b/src/test/regress/expected/local_shard_execution.out
@@ -1674,7 +1674,7 @@ RESET client_min_messages;
 RESET citus.log_local_commands;
 \c - - - :master_port
 SET citus.next_shard_id TO 1480000;
--- local execution with custom type
+-- test both local and remote execution with custom type
 SET citus.replication_model TO "streaming";
 SET citus.shard_replication_factor TO 1;
 CREATE TYPE invite_resp AS ENUM ('yes', 'no', 'maybe');
@@ -1690,6 +1690,273 @@ SELECT create_distributed_table('event_responses', 'event_id');
 
 (1 row)
 
+INSERT INTO event_responses VALUES (1, 1, 'yes'), (2, 2, 'yes'), (3, 3, 'no'), (4, 4, 'no');
+CREATE OR REPLACE FUNCTION regular_func(p invite_resp)
+RETURNS int AS $$
+DECLARE
+	q1Result INT;
+	q2Result INT;
+	q3Result INT;
+BEGIN
+SELECT count(*) INTO q1Result FROM event_responses WHERE response = $1;
+SELECT count(*) INTO q2Result FROM event_responses e1 LEFT JOIN event_responses e2 USING (event_id) WHERE e2.response = $1;
+SELECT count(*) INTO q3Result FROM (SELECT * FROM event_responses WHERE response = $1 LIMIT 5) as foo;
+RETURN  q3Result+q2Result+q1Result;
+END;
+$$ LANGUAGE plpgsql;
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+SELECT regular_func('yes');
+ regular_func
+---------------------------------------------------------------------
+            6
+(1 row)
+
+CREATE OR REPLACE PROCEDURE regular_procedure(p invite_resp)
+AS $$
+BEGIN
+PERFORM * FROM event_responses WHERE response = $1;
+PERFORM * FROM event_responses e1 LEFT JOIN event_responses e2 USING (event_id) WHERE e2.response = $1;
+PERFORM  * FROM (SELECT * FROM event_responses WHERE response = $1 LIMIT 5) as foo;
+END;
+$$ LANGUAGE plpgsql;
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+PREPARE multi_shard_no_dist_key(invite_resp) AS select * from event_responses where response = $1::invite_resp LIMIT 1;
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE multi_shard_no_dist_key('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+PREPARE multi_shard_with_dist_key(int, invite_resp) AS select * from event_responses where event_id > $1 AND response = $2::invite_resp LIMIT 1;
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        2 |       2 | yes
+(1 row)
+
+PREPARE query_pushdown_no_dist_key(invite_resp) AS select * from event_responses e1 LEFT JOIN event_responses e2 USING(event_id) where e1.response = $1::invite_resp LIMIT 1;
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+EXECUTE query_pushdown_no_dist_key('yes');
+ event_id | user_id | response | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes      |       1 | yes
+(1 row)
+
+PREPARE insert_select_via_coord(invite_resp) AS INSERT INTO event_responses SELECT * FROM event_responses where response = $1::invite_resp LIMIT 1 ON CONFLICT (event_id, user_id) DO NOTHING ;
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+PREPARE insert_select_pushdown(invite_resp) AS INSERT INTO event_responses SELECT * FROM event_responses where response = $1::invite_resp ON CONFLICT (event_id, user_id) DO NOTHING;
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+PREPARE router_select_with_no_dist_key_filter(invite_resp) AS select * from event_responses where event_id = 1 AND response = $1::invite_resp LIMIT 1;
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+EXECUTE router_select_with_no_dist_key_filter('yes');
+ event_id | user_id | response
+---------------------------------------------------------------------
+        1 |       1 | yes
+(1 row)
+
+-- rest of the tests assume the table is empty
+TRUNCATE event_responses;
 CREATE OR REPLACE PROCEDURE register_for_event(p_event_id int, p_user_id int, p_choice invite_resp)
 LANGUAGE plpgsql AS $fn$
 BEGIN
diff --git a/src/test/regress/sql/local_shard_execution.sql b/src/test/regress/sql/local_shard_execution.sql
index 8a102780d..a18ab177a 100644
--- a/src/test/regress/sql/local_shard_execution.sql
+++ b/src/test/regress/sql/local_shard_execution.sql
@@ -846,7 +846,7 @@ RESET citus.log_local_commands;
 
 \c - - - :master_port
 SET citus.next_shard_id TO 1480000;
--- local execution with custom type
+-- test both local and remote execution with custom type
 SET citus.replication_model TO "streaming";
 SET citus.shard_replication_factor TO 1;
 CREATE TYPE invite_resp AS ENUM ('yes', 'no', 'maybe');
@@ -860,6 +860,105 @@ CREATE TABLE event_responses (
 
 SELECT create_distributed_table('event_responses', 'event_id');
 
+INSERT INTO event_responses VALUES (1, 1, 'yes'), (2, 2, 'yes'), (3, 3, 'no'), (4, 4, 'no');
+
+CREATE OR REPLACE FUNCTION regular_func(p invite_resp)
+RETURNS int AS $$
+DECLARE
+	q1Result INT;
+	q2Result INT;
+	q3Result INT;
+BEGIN
+SELECT count(*) INTO q1Result FROM event_responses WHERE response = $1;
+SELECT count(*) INTO q2Result FROM event_responses e1 LEFT JOIN event_responses e2 USING (event_id) WHERE e2.response = $1;
+SELECT count(*) INTO q3Result FROM (SELECT * FROM event_responses WHERE response = $1 LIMIT 5) as foo;
+RETURN  q3Result+q2Result+q1Result;
+END;
+$$ LANGUAGE plpgsql;
+
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+SELECT regular_func('yes');
+
+CREATE OR REPLACE PROCEDURE regular_procedure(p invite_resp)
+AS $$
+BEGIN
+PERFORM * FROM event_responses WHERE response = $1;
+PERFORM * FROM event_responses e1 LEFT JOIN event_responses e2 USING (event_id) WHERE e2.response = $1;
+PERFORM  * FROM (SELECT * FROM event_responses WHERE response = $1 LIMIT 5) as foo;
+END;
+$$ LANGUAGE plpgsql;
+
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+CALL regular_procedure('no');
+
+PREPARE multi_shard_no_dist_key(invite_resp) AS select * from event_responses where response = $1::invite_resp LIMIT 1;
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+EXECUTE multi_shard_no_dist_key('yes');
+
+PREPARE multi_shard_with_dist_key(int, invite_resp) AS select * from event_responses where event_id > $1 AND response = $2::invite_resp LIMIT 1;
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+EXECUTE multi_shard_with_dist_key(1, 'yes');
+
+PREPARE query_pushdown_no_dist_key(invite_resp) AS select * from event_responses e1 LEFT JOIN event_responses e2 USING(event_id) where e1.response = $1::invite_resp LIMIT 1;
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+EXECUTE query_pushdown_no_dist_key('yes');
+
+PREPARE insert_select_via_coord(invite_resp) AS INSERT INTO event_responses SELECT * FROM event_responses where response = $1::invite_resp LIMIT 1 ON CONFLICT (event_id, user_id) DO NOTHING ;
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+EXECUTE insert_select_via_coord('yes');
+
+PREPARE insert_select_pushdown(invite_resp) AS INSERT INTO event_responses SELECT * FROM event_responses where response = $1::invite_resp ON CONFLICT (event_id, user_id) DO NOTHING;
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+EXECUTE insert_select_pushdown('yes');
+
+PREPARE router_select_with_no_dist_key_filter(invite_resp) AS select * from event_responses where event_id = 1 AND response = $1::invite_resp LIMIT 1;
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+EXECUTE router_select_with_no_dist_key_filter('yes');
+
+-- rest of the tests assume the table is empty
+TRUNCATE event_responses;
+
 CREATE OR REPLACE PROCEDURE register_for_event(p_event_id int, p_user_id int, p_choice invite_resp)
 LANGUAGE plpgsql AS $fn$
 BEGIN